The Sensitivity of Implied Volatility to Expectations of Jumps in Volatility PDF Download
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Author: Aku Penttinen
Publisher:
ISBN:
Category :
Languages : en
Pages : 59
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Book Description
The apparent bias in implied volatility as a forecast of the subsequently realized volatility is a well-documented empirical puzzle. As suggested by e.g. Feinstein (1989), Jackwerth and Rubinstein (1996), and Bates (1997), we test whether unrealized expectations of jumps in volatility could explain this phenomenon. Our findings show that expectations of infrequently occurring jumps in volatility are priced in implied volatility, which has two important consequences. First, implied volatility will slightly exceed realized volatility most of the time only to be considerably lower than realized volatility during infrequently occurring periods of very high volatility. Second, the slope coefficient in the classic forecasting regression of realized volatility on implied volatility is very sensitive to the discrepancy between the ex ante expected and ex post realized jump frequencies. If the in-sample frequency of positive volatility jumps is lower than ex ante assessed by the market, the slope coefficient will be biased downward and the classic regression test will erroneously reject the hypothesis of no bias even if the market is informationally efficient. Since the inferences of almost all previous studies on the forecasting power of implied volatility have been based on data from a period of historically low volatility, our results provide a rational explanation for the illusory bias in implied volatility.
Author: Aku Penttinen
Publisher:
ISBN:
Category :
Languages : en
Pages : 59
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Book Description
The apparent bias in implied volatility as a forecast of the subsequently realized volatility is a well-documented empirical puzzle. As suggested by e.g. Feinstein (1989), Jackwerth and Rubinstein (1996), and Bates (1997), we test whether unrealized expectations of jumps in volatility could explain this phenomenon. Our findings show that expectations of infrequently occurring jumps in volatility are priced in implied volatility, which has two important consequences. First, implied volatility will slightly exceed realized volatility most of the time only to be considerably lower than realized volatility during infrequently occurring periods of very high volatility. Second, the slope coefficient in the classic forecasting regression of realized volatility on implied volatility is very sensitive to the discrepancy between the ex ante expected and ex post realized jump frequencies. If the in-sample frequency of positive volatility jumps is lower than ex ante assessed by the market, the slope coefficient will be biased downward and the classic regression test will erroneously reject the hypothesis of no bias even if the market is informationally efficient. Since the inferences of almost all previous studies on the forecasting power of implied volatility have been based on data from a period of historically low volatility, our results provide a rational explanation for the illusory bias in implied volatility.
Author: Aku Penttinen
Publisher:
ISBN: 9789515556868
Category :
Languages : en
Pages : 45
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Book Description
Author: Jim Gatheral
Publisher: Wiley
ISBN: 0470068256
Category : Business & Economics
Languages : en
Pages : 208
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Book Description
Praise for The Volatility Surface "I'm thrilled by the appearance of Jim Gatheral's new book The Volatility Surface. The literature on stochastic volatility is vast, but difficult to penetrate and use. Gatheral's book, by contrast, is accessible and practical. It successfully charts a middle ground between specific examples and general models--achieving remarkable clarity without giving up sophistication, depth, or breadth." --Robert V. Kohn, Professor of Mathematics and Chair, Mathematical Finance Committee, Courant Institute of Mathematical Sciences, New York University "Concise yet comprehensive, equally attentive to both theory and phenomena, this book provides an unsurpassed account of the peculiarities of the implied volatility surface, its consequences for pricing and hedging, and the theories that struggle to explain it." --Emanuel Derman, author of My Life as a Quant "Jim Gatheral is the wiliest practitioner in the business. This very fine book is an outgrowth of the lecture notes prepared for one of the most popular classes at NYU's esteemed Courant Institute. The topics covered are at the forefront of research in mathematical finance and the author's treatment of them is simply the best available in this form." --Peter Carr, PhD, head of Quantitative Financial Research, Bloomberg LP Director of the Masters Program in Mathematical Finance, New York University "Jim Gatheral is an acknowledged master of advanced modeling for derivatives. In The Volatility Surface he reveals the secrets of dealing with the most important but most elusive of financial quantities, volatility." --Paul Wilmott, author and mathematician "As a teacher in the field of mathematical finance, I welcome Jim Gatheral's book as a significant development. Written by a Wall Street practitioner with extensive market and teaching experience, The Volatility Surface gives students access to a level of knowledge on derivatives which was not previously available. I strongly recommend it." --Marco Avellaneda, Director, Division of Mathematical Finance Courant Institute, New York University "Jim Gatheral could not have written a better book." --Bruno Dupire, winner of the 2006 Wilmott Cutting Edge Research Award Quantitative Research, Bloomberg LP
Author: Elisa Alós
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: Soku Byoun
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Using a stochastic volatility option pricing model, we show that the implied volatilities of at-the-money options are not necessarily unbiased and that the fixed interval time-series can produce misleading results. Our results do not support the expectations hypothesis: long-term volatilities rise relative to short-term volatilities, but the increases are not matched as predicted by the expectations hypothesis. In addition, an increase in the current long-term volatility relative to the current short-term volatility is followed by a subsequent decline. The results are similar for both foreign currency and the Samp;P 500 stock index options.
Author: Alexey Medvedev
Publisher:
ISBN:
Category :
Languages : en
Pages : 37
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Book Description
Author: Elisa Nicolato
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
We consider a tractable affine stochastic volatility model that generalizes the seminal Heston (1993) model by augmenting it with jumps in the instantaneous variance process. In this framework, we consider options written on the realized variance, and we examine the impact of the distribution of jumps on the associated implied volatility smile. We provide sufficient conditions for the asymptotic behavior of the implied volatility of variance for small and large strikes. In particular, by selecting alternative jump distributions, we show that one can obtain fundamentally different shapes of the implied volatility of variance smile -- some clearly at odds with the upward-sloping volatility skew observed in variance markets.
Author: Colin Bennett
Publisher:
ISBN: 9781461108757
Category :
Languages : en
Pages : 316
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Book Description
This publication aims to fill the void between books providing an introduction to derivatives, and advanced books whose target audience are members of quantitative modelling community. In order to appeal to the widest audience, this publication tries to assume the least amount of prior knowledge. The content quickly moves onto more advanced subjects in order to concentrate on more practical and advanced topics. "A master piece to learn in a nutshell all the essentials about volatility with a practical and lively approach. A must read!" Carole Bernard, Equity Derivatives Specialist at Bloomberg "This book could be seen as the 'volatility bible'!" Markus-Alexander Flesch, Head of Sales & Marketing at Eurex "I highly recommend this book both for those new to the equity derivatives business, and for more advanced readers. The balance between theory and practice is struck At-The-Money" Paul Stephens, Head of Institutional Marketing at CBOE "One of the best resources out there for the volatility community" Paul Britton, CEO and Founder of Capstone Investment Advisors "Colin has managed to convey often complex derivative and volatility concepts with an admirable simplicity, a welcome change from the all-too-dense tomes one usually finds on the subject" Edmund Shing PhD, former Proprietary Trader at BNP Paribas "In a crowded space, Colin has supplied a useful and concise guide" Gary Delany, Director Europe at the Options Industry Council
Author: Michael S. Johannes
Publisher:
ISBN:
Category :
Languages : en
Pages : 47
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Book Description
This paper examines a class of continuous-time models that incorporate jumps in returns and volatility, in addition to diffusive stochastic volatility. We develop a likelihood-based estimation strategy and provide estimates of model parameters, spot volatility, jump times and jump sizes using both Samp;P 500 and Nasdaq 100 index returns. Estimates of jumps times, jump sizes and volatility are particularly useful for disentangling the dynamic effects of these factors during periods of market stress, such as those in 1987, 1997 and 1998. Using both formal and informal diagnostics, we find strong evidence for jumps in volatility, even after accounting for jumps in returns. We use implied volatility curves computed from option prices to judge the economic differences between the models. Finally, we evaluate the impact of estimation risk on option prices and find that the uncertainty in estimating the parameters and the spot volatility has important, though very different, effects on option prices.
Author: Monique W.M. Donders
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
We study the implied volatility behavior of European Options Exchange call option prices around scheduled news announcement days of the underlying stock. Implied volatilities significantly increase during the pre-event period and reach a maximum at the eve of the news announcement. After the news release, the implied volatility drops sharply and is at its minimum four days after the news release. From that point on it gradually moves back to its long run level. These results also hold if implied volatilities are corrected for market-wide changes in volatility by subtracting the implied volatility of the EOE-index or the average implied volatility of a group of control stocks. The volatility of the underlying stocks does not change during the pre- and post-event period. Only at the event date itself movements in the price of the underlying stock are significantly larger than expected, given mean and standard deviation of the stock returns in the control period. Hence, volatility of the underlying assets seems to be higher only on event days. We give an option pricing model based on this one-time jump in volatility. The model implicates a pattern of changes in implied volatilities that roughly agrees with the above described pattern. We test two trading strategies that may profit from the movements in implied volatilities and find that the results are statistically insignificant.
