Volatility Is Rough

Jim Gatheral, Thibault Jaisson, Mathieu Rosenbaum · Quantitative Finance / arXiv · 2018 · quantitative-finance · 10.1080/14697688.2017.1393551 · record gatheral2018-rough-volatility
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Where this record's text came from. faceted 2026-08 by reading the locally held text (pdftext); every evidence string verified as an exact substring of that text before merging. Claim type is 'existence' because the headline claim is that a property (roughness, H ≈ 0.1) is present in observed volatility; the paper additionally contains a critique strand (spurious long memory) and a mechanism strand (Hawkes-process order splitting as the microstructural origin), neither of which the single-valued facet can carry. method is 'observational-study' since the primary evidence is estimation on market high-frequency and realized-variance data (DAX, Bund, S&P, NASDAQ and the Oxford-Man indices); the paper also uses Monte Carlo simulation for bias checks and includes short appendix proofs, so it is genuinely mixed-method. Quotes were taken from lines free of the page numbers and footnote markers that the PDF extraction interleaves into sentences. 2026-08-14, 2026-08-16 and 2026-08-25 schema-0.3 passes: every quote verified as an exact substring of the staged text and anchored at merge time; concept terms verified present; every edge endpoint an existing node. Update, 16 September 2026: EXCEPTION TO THE DATED PASS ABOVE, on this record only: this record carries 1 composite quote field - a quote assembled from two or more passages joined by an ellipsis. A COMPOSITE IS NOT AN EXACT CONTIGUOUS SUBSTRING of the staged text and is deliberately not anchored: each of its parts is verified separately at the offsets in evidence composite spans, and a part occurring more than once carries span null rather than a guessed offset. So the 'every quote verified as an exact substring' clause of the dated pass above DOES NOT HOLD for those fields, and never did - the parts were verified, the whole was not. Nothing is deleted, re-grounded or withdrawn: this writes down an exception that was always true of composites and had not been recorded, so a reader was told more than the pass had checked. 2026-09-16 the project CORRECTION TO THE EXEMPTION ABOVE, SAME DAY: THE EXEMPTION DOES NOT APPLY TO THIS RECORD. Its evidence composite spans row(s) are FOSSILS of a 2026-08-25 composite marking that was superseded by a 2026-08-26 re-slice; the quote is an exact contiguous substring of the staged text, so the dated substring claim above holds for it WITHOUT exception. The clause is left in place with this correction beside it rather than removed, so that the error and its repair are both on the record.

Some words in these quotes contain the wrong character. The PDF this text was extracted from substituted 37 characters inside a word — a currency sign or a stray accent where a letter pair belongs, as in signi¢cantly for significantly, or a single ligature glyph, as in conﬁdence. They are valid characters in the wrong place, so they survive every encoding check. The quotes keep them for the same reason as above, and a search of this page will not find the affected words.

1 quote on this page was cut from a different copy of this article. This project holds two extractions of this paper: the plain text every other quote here is anchored in, and the publisher’s own HTML edition, which we are not licensed to republish. It is verbatim in the second and cannot be found in the first — not because the tagging is wrong, but because the extraction damaged the passage: a page number dropped into the middle of a number, a formula moved out of its sentence, a ligature where two letters belong. The record names the copy for each one. The quote is the paper’s; the extraction is not.

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Other fields define these differently the same word, defined another way in another discipline
memory 23 fields · sample-size 5 fields · integration 3 fields · linear regression 2 fields · variance 2 fields

Tags on this paper

Every tag the record carries, each linking to every other paper in the corpus that carries it. A tag appears here whether or not its words occur in the article — the spans below are only the ones a sentence in this paper licenses. Of the 125 concept tags on this paper, 122 are grounded in a quoted sentence. 116 carry the tagger's gloss of what the term means in this paper, which is not something the article can license.

stochastic volatility fractional Brownian motion Hurst exponent realized volatility power law long memory Hurst parameter spot volatility volatility surface continuous semimartingales volatility process Black-Scholes framework deterministic function of time local volatility model time-inhomogeneous future volatility surfaces exotic options stochastic volatility models continuous Brownian semi-martingale local volatility dynamics stochastic volatility dynamics local-stochastic-volatility (LSV) models reasonable dynamics slow decay of the autocorrelation function not integrable power-law with exponent less than 1 asymptotic behavior of the covariance function usual time scales of observation dependence structure implied volatility volatility parameter market price of that option strike price time to expiry power-law function of time to expiry term structure of at-the-money (ATM) skew sum of decaying exponentials explosion of the volatility smile presence of jumps ATM volatility skew smoothness parameter increments of the log-volatility approximately normally distributed monofractal scaling property fractional stochastic volatility (FSV) model Rough FSV (RSFV) Rough FSV RFSV FSV Rough FSV (RFSV) RFSV model improved forecasts of realized volatility volatility persistence classical statistical procedures RFSV volatility forecasts conventional AR and HAR volatility forecasts market microstructure explanation high degree of endogeneity of the market algorithmic trading integrated variance model with uncertainty zones very short time intervals daily realized variance estimates Oxford-Man Institute of Quantitative Finance Realized Library integration biased upwards smoothness parameter sq regressing log m(q, ∆) against log ∆ fractional Ornstein-Uhlenbeck process mathematical tractability reasonableness of the model at very large times very long reversion time scale choice H < 1/2 observed smoothness of the volatility process term structure of volatility skew mean reversion by practitioners fBM like-behavior of the log-volatility stationarity property one-hour window daily eight-hour windows regularizing effect of the integral operator volatility of volatility persistent periods of high volatility low volatility periods fractal-type behavior range of observation scales volatility process over one day volatility process over a decade straight lines with slope 1.86 power law behavior of the autocorrelation function wrongly convinced classical estimation procedures spurious long memory of volatility classical power law sense RFSV forecast AR and HAR forecasts longer horizons more parsimonious forecast time horizon relevant regression window forecasting horizon volatility over the last week volatility over the last month Hawkes processes extensions of Poisson processes intensity at a given time past jumps point process kernel L1 norm power law tail degree of endogeneity of the market one given order many other orders electronic high frequency trading splitting of large orders metaorder superposition effect irregular volatility macroscopic scaling limit of Hawkes processes integrated fractional process cumulated order flow Rough Fractional Stochastic Volatility (RFSV) model FSV model one major difference THE TERM'S TWO SENSES ARE SEPARATED BY THEIR HISTORY: 'long memory' initially meant the slow decay of the autocorrelation function - anything slower than exponential - and over time acquired the more precise meaning that the function is not integrable, and more precisely still that it decays as a power law with exponent less than one THE TECHNICAL SENSE IS DEFENDED AS THE ONLY ESTIMABLE ONE: the recent literature assumes long memory in the technical sense, and the authors add that meaningful results can probably ONLY be obtained under such a specification, since the asymptotic behaviour of the covariance function cannot be estimated without assuming a specific form for it THE QUESTION IS DECLARED UNANSWERABLE AS POSED, and the authors then supply a different instrument rather than a different answer: stated in terms of the asymptotic behaviour of the autocorrelation function the long memory question simply cannot be answered, but explicit expressions still allow the dependence structure to be analysed A WIDELY ACCEPTED STYLIZED FACT IS EXPLAINED AS AN ARTEFACT OF ITS OWN DETECTOR: the model has no long memory property, and yet the classical statistical procedures designed to detect volatility persistence TEND TO CONCLUDE THAT LONG MEMORY IS PRESENT in data the model generated the evidence for the stylized fact is dated rather than dismissed: the analyses supporting it use data that PREDATE high-frequency electronic trading, and the authors note the evidence has never satisfied the remaining doubters THE NEW NAME IS CHOSEN TO CARRY THE DEPARTURE: an existing model is adopted and renamed, with the new word picked to underline the single parameter inequality that separates it from its parent in the process used, ONE PARAMETER CONTROLS BOTH PROPERTIES AT ONCE - regularity and long memory stand in one-to-one correspondence through the Hurst parameter - so a claim about smoothness is inseparably a claim about memory A WIDESPREAD BELIEF IS MET WITH A COUNTEREXAMPLE RATHER THAN AN ARGUMENT: the model is offered as a counterexample to the widespread belief that the explosion of the volatility smile at short expiries implies the presence of jumps THE MODEL IS OFFERED AGAINST TWO SEPARATE REQUIREMENTS rather than one - consistency with the empirically observed properties of the volatility time series AND consistency with the shape of the volatility surface - and the claim is stated as POTENTIAL, not as achievement the smoothness estimate is reported as a RANGE ACROSS ASSETS rather than a single fitted number, and it is accompanied by two further empirical properties of the increments - approximate normality and a monofractal scaling of the moments - which together are what licenses the modelling choice volatility fractional Brownian Hurst log-volatility exponent memory realized rough Hurst parameter H mean mean of regression linear regression sample-size sample size standard-error standard error variance observational-study

Legend

relation to other work	`claim_relations`	how this paper stands to another: agrees, contradicts, extends, qualifies
claim type	`claim_type`	the shape of the claim: existence, mechanism, method, critique, prediction, null
concept edge	`concept_edges`	an asserted relation between two concepts, with the sentence asserting it
concept	`concepts`	an idea the paper works with, quoted where the paper uses it
content tag	`content_tags`	a finding, definition, quantity, statistic or variable named in the paper
control	`controls`	an experiment run to eliminate a rival explanation
limitation	`limitations`	what the paper says its evidence cannot support
mechanism	`mechanisms`	how the reported effect is said to come about
method	`method`	how the paper produced its evidence
phenomenon	`phenomenon`	the effect or regularity under study
sense	`senses`	a distinct use of a term, quoted where the paper fixes it
transfer	`transfers`	a method or concept carried in from another field
unrecordable relation	`unhoused_relations`	a relation the paper asserts that this vocabulary cannot express, with the reason

The paper

The full text is not reproduced here. This article is not cleared for redistribution, so the page carries the tag layer only. Its evidence sentences are withheld; the grounding status remains with each tag, and the article itself is at https://doi.org/10.1080/14697688.2017.1393551. The reading view exists for the papers whose licence permits it.

Every tag on this page

claim_relations 6 · claim_type 1 · concept_edges 11 · concepts 122 · content_tags 12 · controls 1 · limitations 7 · mechanisms 10 · method 1 · phenomenon 1 · senses 22 · transfers 1 · unhoused_relations 6

Relations on this page carry a quotation for the claim. Where a relation was separately evidenced — and so tested against the vocabulary for its type — the row says so; 9 of 11 relations here carry that mark. The rest are the tagger’s reading of the sentence quoted beside them.

facet	tag	field	conf.	whose words
claim_type	existence Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`claim_type`		the paper's words
phenomenon	smoothness (roughness) of the volatility process Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`phenomenon`		the paper's words
method	observational-study Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: observational-study	`method`		the paper's words
mechanisms	mechanisms Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: THE TERM'S TWO SENSES ARE SEPARATED BY THEIR HISTORY: 'long memory' initially meant the slow decay of the autocorrelation function - anything slower than exponential - and over time acquired the more precise meaning that the function is not integrable, and more precisely still that it decays as a power law with exponent less than one	`mechanisms[0]`	0.95	the tagger's words
mechanisms	mechanisms Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: THE TECHNICAL SENSE IS DEFENDED AS THE ONLY ESTIMABLE ONE: the recent literature assumes long memory in the technical sense, and the authors add that meaningful results can probably ONLY be obtained under such a specification, since the asymptotic behaviour of the covariance function cannot be estimated without assuming a specific form for it	`mechanisms[1]`	0.85	the tagger's words
mechanisms	mechanisms Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. about this quote: Span re-sliced at drafting: the staged text splices footnote 1 AND a page number between 'This implies' and its own subordinate clause ('…see Section 2.1. 3 that when stated in term…'), so the quote begins after the splice. Extraction damage, not authorial. Damage class C. also in: THE QUESTION IS DECLARED UNANSWERABLE AS POSED, and the authors then supply a different instrument rather than a different answer: stated in terms of the asymptotic behaviour of the autocorrelation function the long memory question simply cannot be answered, but explicit expressions still allow the dependence structure to be analysed	`mechanisms[2]`	0.85	the tagger's words
mechanisms	mechanisms Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: A WIDELY ACCEPTED STYLIZED FACT IS EXPLAINED AS AN ARTEFACT OF ITS OWN DETECTOR: the model has no long memory property, and yet the classical statistical procedures designed to detect volatility persistence TEND TO CONCLUDE THAT LONG MEMORY IS PRESENT in data the model generated	`mechanisms[3]`	0.95	the tagger's words
mechanisms	mechanisms Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: the evidence for the stylized fact is dated rather than dismissed: the analyses supporting it use data that PREDATE high-frequency electronic trading, and the authors note the evidence has never satisfied the remaining doubters	`mechanisms[4]`	0.95	the tagger's words
mechanisms	mechanisms Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: THE NEW NAME IS CHOSEN TO CARRY THE DEPARTURE: an existing model is adopted and renamed, with the new word picked to underline the single parameter inequality that separates it from its parent	`mechanisms[5]`	0.85	the tagger's words
mechanisms	mechanisms Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: in the process used, ONE PARAMETER CONTROLS BOTH PROPERTIES AT ONCE - regularity and long memory stand in one-to-one correspondence through the Hurst parameter - so a claim about smoothness is inseparably a claim about memory	`mechanisms[6]`	0.95	the tagger's words
mechanisms	mechanisms Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: A WIDESPREAD BELIEF IS MET WITH A COUNTEREXAMPLE RATHER THAN AN ARGUMENT: the model is offered as a counterexample to the widespread belief that the explosion of the volatility smile at short expiries implies the presence of jumps	`mechanisms[7]`	0.85	the tagger's words
mechanisms	mechanisms Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: THE MODEL IS OFFERED AGAINST TWO SEPARATE REQUIREMENTS rather than one - consistency with the empirically observed properties of the volatility time series AND consistency with the shape of the volatility surface - and the claim is stated as POTENTIAL, not as achievement	`mechanisms[8]`	0.85	the tagger's words
mechanisms	mechanisms Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. about this quote: The span contains 'H¨older' for 'Hölder' - the diaeresis is emitted BEFORE its base letter by the PDF extraction. The quote is still an exact substring and anchors correctly; the damage is in what a reader of the tag sees, not in the provenance. None of the four shapes an internal tool looks for covers this, so it is annotated by hand. also in: the smoothness estimate is reported as a RANGE ACROSS ASSETS rather than a single fitted number, and it is accompanied by two further empirical properties of the increments - approximate normality and a monofractal scaling of the moments - which together are what licenses the modelling choice	`mechanisms[9]`	0.95	the tagger's words
limitations	the scaling result is established at usual observation time scales Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. what this limits: the scaling result, over the range examined: AT LEAST AT USUAL TIME SCALES OF OBSERVATION	`limitations[0]`		the tagger's words
limitations	Smoothness estimates based on whole-trading-day realized variance are expected to be biased upwards because integration smooths the process. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. what this limits: the smoothness estimates specifically: WE EXPECT ESTIMATES OF THE SMOOTHNESS OF THE VOLATILITY PROCESS TO BE BIASED UPWARDS, INTEGRATION BEING A REG[ularising operation] - the direction of the bias is stated	`limitations[1]`		the tagger's words
limitations	Volatility is never observed directly, so the key quantity m(q, Δ) can only be computed from proxies. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. what this limits: every quantity computed in the paper: THE VOLATILITY PROCESS IS NOT DIRECTLY OBSERVABLE, AND AN EXACT COMPUTATION OF m(q, delta) IS NOT POSSIBLE IN PRACTICE	`limitations[2]`		the tagger's words
limitations	The paper only treats the volatility time series; whether the model is consistent with observed option prices is deferred. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. what this limits: the option-pricing implications: A MORE DETAILED ANALYSIS OF THE CONSISTENCY OF OUR MODEL WITH OPTION PRICES IS LEFT FOR A FUTURE ARTICLE	`limitations[3]`		the tagger's words
limitations	The property cannot be estimated without first assuming the functional form whose presence is at issue. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. what this limits: any estimate of long memory in volatility: the asymptotic behaviour of the covariance function cannot be estimated without assuming a specific form for it, so the specification is an input to the result rather than an output	`limitations[4]`	1.0	the tagger's words
limitations	As the term is now defined, the field's central question about volatility cannot be answered at all. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. what this limits: the debate over whether volatility has long memory: stated in terms of the asymptotic behaviour of the autocorrelation function, the paper says the question simply cannot be answered	`limitations[5]`	1.0	the tagger's words
limitations	Standard procedures report the property in data generated by a model that does not have it, which the authors offer as the reason the field accepted it as a stylized fact. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. what this limits: the widely accepted stylized fact that volatility has long memory: classical procedures for detecting volatility persistence conclude it is present in data simulated from a model that has no long memory property at all	`limitations[6]`	1.0	the tagger's words
transfers	fractional Brownian motion with a Hurst exponent below 1/2 used as the model of log-volatility, in place of the standard semimartingale volatility models of finance Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`transfers[0]`	0.9	the tagger's words
controls	a detailed test of the model against observed option prices - NOT performed, and deferred to a future article Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. eliminates: the model fitting volatility time series while failing on the option prices it would be used to compute, which is the comparison the paper itself says its predecessors fail · outcome (stated by the tagger, no quotation): absent-declared-unreported	`controls[0]`	0.85	the tagger's words
concepts	fractional Brownian motion Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: fractional Brownian motion	`concepts[1]`		the paper's words
concepts	realized volatility Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: realized volatility	`concepts[3]`		the paper's words
concepts	long memory Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: long memory	`concepts[5]`		the paper's words
concepts	Hurst parameter Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: Hurst parameter	`concepts[6]`		the paper's words
concepts	spot volatility Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: spot volatility	`concepts[7]`		the paper's words
concepts	volatility surface Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: volatility surface	`concepts[8]`		the paper's words
concepts	continuous semimartingales Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: continuous semimartingales	`concepts[9]`	0.95	the paper's words
concepts	volatility process Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: volatility process	`concepts[10]`	0.95	the paper's words
concepts	Black-Scholes framework Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: Black-Scholes framework	`concepts[11]`	0.95	the paper's words
concepts	deterministic function of time Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: deterministic function of time	`concepts[12]`	0.95	the paper's words
concepts	local volatility model Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: local volatility model	`concepts[13]`	0.95	the paper's words
concepts	time-inhomogeneous Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: time-inhomogeneous	`concepts[14]`	0.95	the paper's words
concepts	future volatility surfaces Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: future volatility surfaces	`concepts[15]`	0.95	the paper's words
concepts	exotic options Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: exotic options	`concepts[16]`	0.95	the paper's words
concepts	stochastic volatility models Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: stochastic volatility models	`concepts[17]`	0.95	the paper's words
concepts	continuous Brownian semi-martingale Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: continuous Brownian semi-martingale	`concepts[18]`	0.95	the paper's words
concepts	local volatility dynamics Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: local volatility dynamics	`concepts[19]`	0.95	the paper's words
concepts	stochastic volatility dynamics Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: stochastic volatility dynamics	`concepts[20]`	0.95	the paper's words
concepts	local-stochastic-volatility (LSV) models Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: local-stochastic-volatility (LSV) models	`concepts[21]`	0.95	the paper's words
concepts	reasonable dynamics Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: reasonable dynamics	`concepts[22]`	0.95	the paper's words
concepts	slow decay of the autocorrelation function Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: slow decay of the autocorrelation function	`concepts[23]`	0.95	the paper's words
concepts	not integrable Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: not integrable	`concepts[24]`	0.95	the paper's words
concepts	power-law with exponent less than 1 Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: power-law with exponent less than 1	`concepts[25]`	0.95	the paper's words
concepts	asymptotic behavior of the covariance function Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: asymptotic behavior of the covariance function	`concepts[26]`	0.95	the paper's words
concepts	usual time scales of observation Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: usual time scales of observation	`concepts[27]`	0.95	the paper's words
concepts	dependence structure Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. about this quote: PAGE FURNITURE IS SPLICED INTO THE 'evidence' QUOTE - the text of footnote 1 ('1Actually H corresponds…') and a page number, between 'This implies' and 'that when stated'. The words on either side of it were never continuous on the page; read the quote with it deleted. also in: dependence structure	`concepts[28]`	0.95	the paper's words
concepts	implied volatility Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: implied volatility	`concepts[29]`	0.95	the paper's words
concepts	volatility parameter Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: volatility parameter	`concepts[30]`	0.95	the paper's words
concepts	market price of that option Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: market price of that option	`concepts[31]`	0.95	the paper's words
concepts	strike price Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: strike price	`concepts[32]`	0.95	the paper's words
concepts	time to expiry Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: time to expiry	`concepts[33]`	0.95	the paper's words
concepts	power-law function of time to expiry Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: power-law function of time to expiry	`concepts[34]`	0.95	the paper's words
concepts	term structure of at-the-money (ATM) skew Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: term structure of at-the-money (ATM) skew	`concepts[35]`	0.95	the paper's words
concepts	sum of decaying exponentials Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: sum of decaying exponentials	`concepts[36]`	0.95	the paper's words
concepts	explosion of the volatility smile Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: explosion of the volatility smile	`concepts[37]`	0.95	the paper's words
concepts	presence of jumps Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: presence of jumps	`concepts[38]`	0.95	the paper's words
concepts	ATM volatility skew Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: ATM volatility skew	`concepts[39]`	0.95	the paper's words
concepts	smoothness parameter Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: smoothness parameter	`concepts[40]`	0.95	the paper's words
concepts	increments of the log-volatility Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: increments of the log-volatility	`concepts[41]`	0.95	the paper's words
concepts	approximately normally distributed Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: approximately normally distributed	`concepts[42]`	0.95	the paper's words
concepts	monofractal scaling property Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: monofractal scaling property	`concepts[43]`	0.95	the paper's words
concepts	fractional stochastic volatility (FSV) model Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: fractional stochastic volatility (FSV) model	`concepts[44]`	0.95	the paper's words
concepts	Rough FSV (RSFV) Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: Rough FSV (RSFV)	`concepts[45]`	0.95	the paper's words
concepts	Rough FSV Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: Rough FSV	`concepts[46]`	0.95	the paper's words
concepts	RFSV Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: RFSV	`concepts[47]`	0.95	the paper's words
concepts	FSV Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: FSV	`concepts[48]`	0.95	the paper's words
concepts	Rough FSV (RFSV) Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: Rough FSV (RFSV)	`concepts[49]`	0.95	the paper's words
concepts	RFSV model Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: RFSV model	`concepts[50]`	0.95	the paper's words
concepts	improved forecasts of realized volatility Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: improved forecasts of realized volatility	`concepts[51]`	0.95	the paper's words
concepts	volatility persistence Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: volatility persistence	`concepts[52]`	0.95	the paper's words
concepts	classical statistical procedures Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: classical statistical procedures	`concepts[53]`	0.95	the paper's words
concepts	RFSV volatility forecasts Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: RFSV volatility forecasts	`concepts[54]`	0.95	the paper's words
concepts	conventional AR and HAR volatility forecasts Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: conventional AR and HAR volatility forecasts	`concepts[55]`	0.95	the paper's words
concepts	market microstructure explanation Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: market microstructure explanation	`concepts[56]`	0.95	the paper's words
concepts	high degree of endogeneity of the market Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: high degree of endogeneity of the market	`concepts[57]`	0.95	the paper's words
concepts	algorithmic trading Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: algorithmic trading	`concepts[58]`	0.95	the paper's words
concepts	integrated variance Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: integrated variance	`concepts[59]`	0.95	the paper's words
concepts	model with uncertainty zones Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: model with uncertainty zones	`concepts[60]`	0.95	the paper's words
concepts	very short time intervals Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: very short time intervals	`concepts[61]`	0.95	the paper's words
concepts	daily realized variance estimates Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: daily realized variance estimates	`concepts[62]`	0.95	the paper's words
concepts	Oxford-Man Institute of Quantitative Finance Realized Library Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: Oxford-Man Institute of Quantitative Finance Realized Library	`concepts[63]`	0.95	the paper's words
concepts	integration Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: integration	`concepts[64]`	0.95	the paper's words
concepts	biased upwards Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: biased upwards	`concepts[65]`	0.95	the paper's words
concepts	smoothness parameter sq Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: smoothness parameter sq	`concepts[66]`	0.95	the paper's words
concepts	regressing log m(q, ∆) against log ∆ Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: regressing log m(q, ∆) against log ∆	`concepts[67]`	0.95	the paper's words
concepts	fractional Ornstein-Uhlenbeck process Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: fractional Ornstein-Uhlenbeck process	`concepts[68]`	0.95	the paper's words
concepts	mathematical tractability Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: mathematical tractability	`concepts[69]`	0.95	the paper's words
concepts	reasonableness of the model at very large times Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: reasonableness of the model at very large times	`concepts[70]`	0.95	the paper's words
concepts	very long reversion time scale Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: very long reversion time scale	`concepts[71]`	0.95	the paper's words
concepts	choice H < 1/2 Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: choice H < 1/2	`concepts[72]`	0.95	the paper's words
concepts	observed smoothness of the volatility process Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: observed smoothness of the volatility process	`concepts[73]`	0.95	the paper's words
concepts	term structure of volatility skew Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: term structure of volatility skew	`concepts[74]`	0.95	the paper's words
concepts	mean reversion by practitioners Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: mean reversion by practitioners	`concepts[75]`	0.95	the paper's words
concepts	fBM like-behavior of the log-volatility Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: fBM like-behavior of the log-volatility	`concepts[76]`	0.95	the paper's words
concepts	stationarity property Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: stationarity property	`concepts[77]`	0.95	the paper's words
concepts	one-hour window Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: one-hour window	`concepts[78]`	0.95	the paper's words
concepts	daily eight-hour windows Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: daily eight-hour windows	`concepts[79]`	0.95	the paper's words
concepts	regularizing effect of the integral operator Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: regularizing effect of the integral operator	`concepts[80]`	0.95	the paper's words
concepts	volatility of volatility Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: volatility of volatility	`concepts[81]`	0.95	the paper's words
concepts	persistent periods of high volatility Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: persistent periods of high volatility	`concepts[82]`	0.95	the paper's words
concepts	low volatility periods Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: low volatility periods	`concepts[83]`	0.95	the paper's words
concepts	fractal-type behavior Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: fractal-type behavior	`concepts[84]`	0.95	the paper's words
concepts	range of observation scales Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: range of observation scales	`concepts[85]`	0.95	the paper's words
concepts	volatility process over one day Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: volatility process over one day	`concepts[86]`	0.95	the paper's words
concepts	volatility process over a decade Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: volatility process over a decade	`concepts[87]`	0.95	the paper's words
concepts	straight lines with slope 1.86 Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: straight lines with slope 1.86	`concepts[88]`	0.95	the paper's words
concepts	power law behavior of the autocorrelation function Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: power law behavior of the autocorrelation function	`concepts[89]`	0.95	the paper's words
concepts	wrongly convinced Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: wrongly convinced	`concepts[90]`	0.95	the paper's words
concepts	classical estimation procedures Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: classical estimation procedures	`concepts[91]`	0.95	the paper's words
concepts	spurious long memory of volatility Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: spurious long memory of volatility	`concepts[92]`	0.95	the paper's words
concepts	classical power law sense Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: classical power law sense	`concepts[93]`	0.95	the paper's words
concepts	RFSV forecast Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: RFSV forecast	`concepts[94]`	0.95	the paper's words
concepts	AR and HAR forecasts Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: AR and HAR forecasts	`concepts[95]`	0.95	the paper's words
concepts	longer horizons Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: longer horizons	`concepts[96]`	0.95	the paper's words
concepts	more parsimonious Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: more parsimonious	`concepts[97]`	0.95	the paper's words
concepts	forecast time horizon Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: forecast time horizon	`concepts[98]`	0.95	the paper's words
concepts	relevant regression window Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: relevant regression window	`concepts[99]`	0.95	the paper's words
concepts	forecasting horizon Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: forecasting horizon	`concepts[100]`	0.95	the paper's words
concepts	volatility over the last week Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: volatility over the last week	`concepts[101]`	0.95	the paper's words
concepts	volatility over the last month Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: volatility over the last month	`concepts[102]`	0.95	the paper's words
concepts	Hawkes processes Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: Hawkes processes	`concepts[103]`	0.95	the paper's words
concepts	extensions of Poisson processes Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: extensions of Poisson processes	`concepts[104]`	0.95	the paper's words
concepts	intensity at a given time Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: intensity at a given time	`concepts[105]`	0.95	the paper's words
concepts	past jumps Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: past jumps	`concepts[106]`	0.95	the paper's words
concepts	point process Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: point process	`concepts[107]`	0.95	the paper's words
concepts	kernel Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: kernel	`concepts[108]`	0.95	the paper's words
concepts	L1 norm Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: L1 norm	`concepts[109]`	0.95	the paper's words
concepts	power law tail Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: power law tail	`concepts[110]`	0.95	the paper's words
concepts	degree of endogeneity of the market Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: degree of endogeneity of the market	`concepts[111]`	0.95	the paper's words
concepts	one given order Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: one given order	`concepts[112]`	0.95	the paper's words
concepts	many other orders Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: many other orders	`concepts[113]`	0.95	the paper's words
concepts	electronic high frequency trading Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: electronic high frequency trading	`concepts[114]`	0.95	the paper's words
concepts	splitting of large orders Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: splitting of large orders	`concepts[115]`	0.95	the paper's words
concepts	metaorder Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: metaorder	`concepts[116]`	0.95	the paper's words
concepts	superposition effect Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: superposition effect	`concepts[117]`	0.95	the paper's words
concepts	irregular volatility Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: irregular volatility	`concepts[118]`	0.95	the paper's words
concepts	macroscopic scaling limit of Hawkes processes Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: macroscopic scaling limit of Hawkes processes	`concepts[119]`	0.95	the paper's words
concepts	integrated fractional process Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: integrated fractional process	`concepts[120]`	0.95	the paper's words
concepts	cumulated order flow Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: cumulated order flow	`concepts[121]`	0.95	the paper's words
concepts	Rough Fractional Stochastic Volatility (RFSV) model Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: Rough Fractional Stochastic Volatility (RFSV) model	`concepts[122]`	0.95	the paper's words
concepts	FSV model Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: FSV model	`concepts[123]`	0.95	the paper's words
concepts	one major difference Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: one major difference	`concepts[124]`	0.95	the paper's words
unhoused_relations	RFSV model → improved forecasts of realized volatility Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. The RFSV model enables improved forecasts of realized volatility. Enables is absent from the eight governed types and is not direct physical causation.	`unhoused_relations[0]`	0.95	the tagger's words
unhoused_relations	classical statistical procedures → long memory Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. Classical persistence diagnostics tend to conclude long memory in data generated by a model that has none. Misidentifies-as is absent from the edge vocabulary.	`unhoused_relations[1]`	0.95	the tagger's words
unhoused_relations	RFSV forecast → AR and HAR forecasts Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. The RFSV forecast consistently outperforms AR and HAR, especially at longer horizons. Outperforms is absent from the eight types and contrast alone would discard the direction of performance.	`unhoused_relations[2]`	0.95	the tagger's words
unhoused_relations	relevant regression window → forecasting horizon Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. The relevant history window is linear in the forecasting horizon. Proportional-to is absent from the governed edge types.	`unhoused_relations[3]`	0.95	the tagger's words
unhoused_relations	macroscopic scaling limit of Hawkes processes → integrated fractional process Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. The near-critical long-tail Hawkes scaling limit can be seen as an integrated fractional process. Scaling-limit-is-represented-by is absent and a plain is-a would overstate an asymptotic result.	`unhoused_relations[4]`	0.95	the tagger's words
unhoused_relations	cumulated order flow → integrated variance Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. The paper reports a linear relation between cumulated order flow and integrated variance. Correlates-with/linearly-related-to is absent from the eight types.	`unhoused_relations[5]`	0.95	the tagger's words
senses	long memory - SENSE 1, THE ORIGINAL AND LOOSE ONE: slow decay of the autocorrelation function, meaning anything slower than exponential Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`senses[0]`	1.0	the tagger's words
senses	long memory - SENSE 2, THE LATER TECHNICAL ONE the field drifted to: a non-integrable autocorrelation function, more precisely one decaying as a power law with exponent below 1, and the recent literature assumes this sense Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`senses[1]`	1.0	the tagger's words
senses	volatility - AS A PROXY, ALWAYS: the process is not directly observable, so every quantity here is computed from an estimated daily stand-in taken at a fixed time of day Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`senses[2]`	1.0	the tagger's words
senses	Local volatility - exact European-option fit with time-inhomogeneous and unrealistic future dynamics Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`senses[3]`	0.95	the tagger's words
senses	Conventional stochastic volatility - more realistic dynamics without exact consistency with observed European option prices Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`senses[4]`	0.95	the tagger's words
senses	Local-stochastic volatility - market hybrid targeting both exact fit and reasonable dynamics Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`senses[5]`	0.95	the tagger's words
senses	Implied volatility - the Black-Scholes volatility input required to reproduce an option's market price Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`senses[6]`	0.95	the tagger's words
senses	Volatility surface - implied volatility plotted across strike price and time to expiry Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`senses[7]`	0.95	the tagger's words
senses	Short-maturity volatility-smile explosion - reproducible without jumps when volatility is fractionally rough Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`senses[8]`	0.95	the tagger's words
senses	Rough FSV - fractional stochastic volatility with H below one half rather than the long-memory H above one half Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`senses[9]`	0.95	the tagger's words
senses	Spot-volatility observation - intrinsically latent and therefore replaced by daily fixed-time proxies Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`senses[10]`	0.95	the tagger's words
senses	Whole-day realized variance - a regularized spot proxy expected to bias smoothness upward Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`senses[11]`	0.95	the tagger's words
senses	Stationary rough-volatility specification - fractional Ornstein-Uhlenbeck process with a very long reversion scale Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`senses[12]`	0.95	the tagger's words
senses	Practitioner mean reversion - unusually high volatility tends down and unusually low volatility tends up Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`senses[13]`	0.95	the tagger's words
senses	Window-length bias - longer integration raises estimated H and lowers estimated volatility-of-volatility Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`senses[14]`	0.95	the tagger's words
senses	RFSV scale resemblance - a daily volatility path qualitatively resembles a decade-long path Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`senses[15]`	0.95	the tagger's words
senses	Spurious memory diagnosis - standard estimators report power-law memory on simulations whose model has none Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`senses[16]`	0.95	the tagger's words
senses	RFSV forecast parsimony - one H parameter rather than horizon-dependent AR/HAR coefficients Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. about this quote: PAGE FURNITURE IS SPLICED INTO THE 'evidence' QUOTE - the text of footnotes 13 and 14 and a page number, between 'requires the parameter' and 'H to forecast'. The words on either side of it were never continuous on the page; read the quote with it deleted.	`senses[17]`	0.95	the tagger's words
senses	Forecast-history rule - past window approximately matches the future horizon Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`senses[18]`	0.95	the tagger's words
senses	Hawkes endogeneity - one order triggers many more as algorithms respond to other participants' orders Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`senses[19]`	0.95	the tagger's words
senses	Order splitting - many observed orders belong to a slowly executed metaorder Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`senses[20]`	0.95	the tagger's words
senses	Microstructural roughness mechanism - near-critical endogenous feedback plus long-tailed order influence produces a fractional macroscopic limit Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`senses[21]`	0.9	the tagger's words
claim_relations	builds-on → fractional Brownian motion (from mathematics/physics) Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`claim_relations[0]`		the tagger's words
claim_relations	builds-on → the fractional stochastic volatility (FSV) model of Comte and Renault [16] Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`claim_relations[1]`		the tagger's words
claim_relations	extends → the FSV model of Comte and Renault [16], modified to H < 1/2 Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`claim_relations[2]`		the tagger's words
claim_relations	contradicts → the accepted stylized fact of power-law long memory in volatility Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`claim_relations[3]`		the tagger's words
claim_relations	replicates → the stylized fact of near-Gaussian log-volatility increments reported by Andersen et al. ([2], [3]) Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`claim_relations[4]`		the tagger's words
claim_relations	builds-on → Fukasawa [25] on the ATM volatility skew generated by fBM-driven volatility Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`claim_relations[5]`		the tagger's words
concept_edges	long memory —operationalised-as→ Hurst parameter Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. strength of the relation: 1 also in: long memory · Hurst parameter	`concept_edges[0]`		the tagger's words
concept_edges	spot volatility —operationalised-as→ realized volatility Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. strength of the relation: 1 Audit 2026-09-28: DOUBTFUL - read against its full span and kept, but the span writes 'daily spot variances' and 'daily realized variance estimates', not 'spot volatility' / 'realized volatility'. also in: spot volatility · realized volatility	`concept_edges[1]`		the tagger's words
concept_edges	stochastic volatility dynamics —contrasted-with→ local volatility dynamics Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. the relation itself is separately evidenced · strength of the relation: 1 · note: The stochastic dynamics are said to be more realistic than local-volatility dynamics, though still price-inconsistent. also in: stochastic volatility dynamics · local volatility dynamics	`concept_edges[2]`	0.95	the tagger's words
concept_edges	power-law function of time to expiry —contrasted-with→ sum of decaying exponentials Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. the relation itself is separately evidenced · strength of the relation: 1 · note: Observed skew is a power law, in contrast to the conventional model's constant/exponential shape. also in: power-law function of time to expiry · sum of decaying exponentials	`concept_edges[3]`	0.95	the tagger's words
concept_edges	Rough FSV —same-as→ RFSV Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. the relation itself is separately evidenced · strength of the relation: 1 · note: The model name is immediately followed by its acronym in parentheses. also in: Rough FSV · RFSV	`concept_edges[4]`	0.95	the tagger's words
concept_edges	Rough FSV (RFSV) —distinct-from→ FSV Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. the relation itself is separately evidenced · strength of the relation: 1 · note: The paper explicitly contrasts the rough H below one-half regime with FSV. also in: Rough FSV (RFSV) · FSV	`concept_edges[5]`	0.95	the tagger's words
concept_edges	choice H < 1/2 —causes→ observed smoothness of the volatility process Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. the relation itself is separately evidenced · strength of the relation: 1 · note: The choice enables the model to reproduce the observed smoothness. also in: choice H < 1/2 · observed smoothness of the volatility process	`concept_edges[6]`	0.95	the tagger's words
concept_edges	choice H < 1/2 —causes→ term structure of volatility skew Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. the relation itself is separately evidenced · strength of the relation: 1 · note: The same choice enables agreement with the observed skew term structure. also in: choice H < 1/2 · term structure of volatility skew	`concept_edges[7]`	0.95	the tagger's words
concept_edges	one given order —causes→ many other orders Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. the relation itself is separately evidenced · strength of the relation: 1 · note: The paper states that one order endogenously generates many others. also in: one given order · many other orders	`concept_edges[8]`	0.95	the tagger's words
concept_edges	superposition effect —causes→ irregular volatility Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. the relation itself is separately evidenced · strength of the relation: 0.6 — the record marks this weak · note: The authors say they believe the combined phenomena induce irregular volatility. Audit 2026-09-28: DOUBTFUL - read against its full span and kept, but 'We believe' the two phenomena lead to the superposition effect; hedged. also in: superposition effect · irregular volatility	`concept_edges[9]`	0.95	the tagger's words
concept_edges	Rough Fractional Stochastic Volatility (RFSV) model —distinct-from→ FSV model Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. the relation itself is separately evidenced · strength of the relation: 1 · note: The models are separated by the explicitly named major difference H below versus above one half. also in: Rough Fractional Stochastic Volatility (RFSV) model · FSV model	`concept_edges[10]`	0.95	the tagger's words
content_tags	H ≈ 0.1 — Hurst exponent of log-volatility (H<1/2 means rough) Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`content_tags.quantities[0]`		the tagger's words
content_tags	H = 1/2 — the classical Brownian-motion boundary case Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`content_tags.quantities[1]`		the tagger's words
content_tags	Log-volatility acts essentially like fractional Brownian motion with a Hurst exponent near 0.1 at any reasonable time scale, which leads to the Rough FSV (RFSV) model with H < 1/2. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`content_tags.findings[0]`	0.85	the tagger's words
content_tags	Although volatility is NOT long-memory under RFSV, classical persistence tests spuriously detect long memory in RFSV-generated data — explaining why long memory became an accepted stylized fact. Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above.	`content_tags.findings[1]`		the tagger's words
content_tags	Hurst parameter H Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: Hurst parameter H	`content_tags.variables[0]`		the tagger's words
content_tags	RFSV model Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: RFSV model	`content_tags.definitions[0]`		the tagger's words
content_tags	EVIDENCE CORRECTED (RE-GROUNDED) · fractional Brownian motion Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. EVIDENCE CORRECTED: RE-GROUNDED. The old span welded 'model the log of volatility using' - Gatheral's OWN model, a fBM with H < 1/2 - to 'motion (fBM for…' 5,695 characters EARLIER, which belongs to Comte and Renault's H > 1/2 model. It conflated the two Hurst regimes, which is the single distinction this paper exists to draw. also in: fractional Brownian motion	`content_tags.definitions[1]`		the tagger's words
content_tags	mean Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. about this quote: THE QUOTE STARTS INSIDE A FORMULA AND ENDS IN A TABLE: it opens on the tail of the flattened expectation symbol that its sentence defines; this copy places that sentence's last words (the period the mean is taken over) before the quote; and after the quote's last words the text runs into the labels of the forecasting results table. also in: mean	`content_tags.statistics[1]`		the tagger's words
content_tags	regression Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: regression	`content_tags.statistics[2]`		the tagger's words
content_tags	sample-size Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. about this quote: QUOTE REPAIRED: the extractor split a hyphen-space and the quote was recorded faithfully with the damage in it, which made it unanchorable. The repaired string is an EXACT SUBSTRING of the staged text - that is why it was accepted, not because a rule produced it. The text as originally recorded is kept in evidence as extracted. also in: sample-size	`content_tags.statistics[3]`		the tagger's words
content_tags	standard-error Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. also in: standard-error	`content_tags.statistics[4]`		the tagger's words
content_tags	variance Quotation withheld — this record is not cleared for redistribution. The sentence is in the paper at the link above. about this quote: A FOOTNOTE CALL SITS INSIDE THIS QUOTE: the '6' between 'the S&P and' and 'NASDAQ indices' is the paper's footnote marker, not part of the sentence; read the quote with it deleted. also in: variance	`content_tags.statistics[6]`		the tagger's words

Interpretive choices

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What was deliberately not tagged, and why, is recorded per paper by the tagger. Where a paper has no such record, this page says so rather than implying that nothing was declined.