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The fractional volatility model and rough volatility [PDF]
International Journal of Theoretical and Applied Finance 26,
2350010 (2023), 2022 The question of the volatility roughness is interpreted in the framework of a data-reconstructed fractional volatility model, where volatility is driven by fractional noise. Some examples are worked out and also, using Malliavin calculus for fractional processes, an option pricing equation and its solution are obtained.
arxiv +3 more sources
How Does the Volatility of Volatility Depend on Volatility? [PDF]
Risks, 2020 We investigate the state dependence of the variance of the instantaneous variance of the S&P 500 index empirically. Time-series analysis of realized variance over a 20-year period shows strong evidence of an elasticity of variance of the variance parameter close to that of a log-normal model, albeit with an empirical autocorrelation function that ...
Sigurd Emil Rømer, Rolf Poulsen
openaire +6 more sources
On the Volatility of Volatility [PDF]
SSRN Electronic Journal, 2006 The Chicago Board Options Exchange (CBOE) Volatility Index, VIX, is calculated based on prices of out-of-the-money put and call options on the S&P 500 index (SPX). Sometimes called the "investor fear gauge," the VIX is a measure of the implied volatility of the SPX, and is observed to be correlated with the 30-day realized volatility of the SPX ...
Stephen D. H. Hsu, Brian M. Murray
openaire +4 more sources
The Volatility of Realized Volatility [PDF]
Econometric Reviews, 2008 In recent years, with the availability of high-frequency financial market data modeling realized volatility has become a new and innovative research direction. The construction of “observable” or realized volatility series from intra-day transaction data and the use of standard time-series techniques has lead to promising strategies for modeling and ...
CORSI, Fulvio +3 more
openaire +8 more sources
Volatility-of-Volatility Risk [PDF]
Journal of Financial and Quantitative Analysis, 2018 We show that market volatility of volatility is a significant risk factor that affects index and volatility index option returns, beyond volatility itself. The volatility and volatility of volatility indices, identified model-free as the VIX and VVIX, respectively, are only weakly related to each other.
Darien Huang +4 more
openaire +5 more sources
From volatility smiles to the volatility of volatility [PDF]
Decisions in Economics and Finance, 2019 The paper reviews models of the option surface and reduced-form models for stochastic volatility in continuous time, under the risk-neutral measure. It defines “forward volatilities,” analogous to forward interest rates in the theory of the term structure, and provides a proof that the forward volatility is a conditional expected value, under the risk ...
Bernard Dumas +3 more
openaire +2 more sources
SSRN Electronic Journal, 2014 Estimating volatility from recent high frequency data, we revisit the question of the smoothness of the volatility process. Our main result is that log-volatility behaves essentially as a fractional Brownian motion with Hurst exponent H of order 0.1, at any reasonable time scale.
Gatheral, Jim +2 more
openaire +6 more sources
Volatility of volatility of financial markets [PDF]
Mathematical and Computer Modelling, 1998 We present empirical evidence for considering volatility of Eurodollar futures as a stochastic process, requiring a generalization of the standard Black-Scholes (BS) model which treats volatility as a constant. We use a previous development of a statistical mechanics of financial markets (SMFM) to model these issues.
L. Ingber, J.K. Wilson
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Volatility and Development [PDF]
The Quarterly Journal of Economics, 2007 Why is GDP growth so much more volatile in poor countries than in rich ones? We identify three possible reasons: (i) poor countries specialize in fewer and more volatile sectors; (ii) poor countries experience more frequent and more severe aggregate shocks (e.g., from macroeconomic policy); and (iii) poor countries' macroeconomic fluctuations are more ...
Miklós Koren +2 more
openaire +6 more sources
Nutrient loss in composting of agroindustrial residues [PDF]
Engenharia Agrícola, 2013 The management of composting may influence the characteristics of the produced compounds. The experiment used three frequencies of plowing, combined with the conditions: with and without coverage of the composting patio, with and without the use of ...
Leocir J. Carneiro +4 more
doaj +1 more source