Implied Volatility Functions
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Implied Volatility Functions
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Author : Bernard Dumas
language : en
Publisher:
Release Date : 1996
Implied Volatility Functions written by Bernard Dumas and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Options (Finance) categories.
Abstract: Black and Scholes (1973) implied volatilities tend to be systematically related to the option's exercise price and time to expiration. Derman and Kani (1994), Dupire (1994), and Rubinstein (1994) attribute this behavior to the fact that the Black-Scholes constant volatility assumption is violated in practice. These authors hypothesize that the volatility of the underlying asset's return is a deterministic function of the asset price and time and develop the deterministic volatility function (DVF) option valuation model, which has the potential of fitting the observed cross-section of option prices exactly. Using a sample of S & P 500 index options during the period June 1988 through December 1993, we evaluate the economic significance of the implied deterministic volatility function by examining the predictive and hedging performance of the DV option valuation model. We find that its performance is worse than that of an ad hoc Black-Scholes model with variable implied volatilities.
Implied Volatility Functions
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Author : Joshua V. Rosenberg
language : en
Publisher:
Release Date : 2008
Implied Volatility Functions written by Joshua V. Rosenberg and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with categories.
Dumas, Fleming, Whaley (DFW, 1998) find that option models based on deterministic volatility functions (DVF) perform poorly because the estimated volatility function is unstable over time. DFW provide evidence that the DVF changes significantly on a weekly basis. This paper proposes a new class of dynamic implied volatility function models (DIVF). This classof models separates a time-invariant implied volatility function from the stochastic state variables that drive changes in the individual implied volatilities. The dynamics of the state variables are modeled explicitly. This framework facilitates consistent pricing and hedging with time-variation in the implied volatility function (IVF). In tests conducted using the full history of Samp;P500 futures option prices, the DIVF model is found to substantially improve pricing performance compared to static implied volatility function models and benchmark pricing models such as Black and Scholes (1973).
Implied Volatility Functions
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Author : Joshua Rosenberg
language : en
Publisher:
Release Date : 1999
Implied Volatility Functions written by Joshua Rosenberg and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Options (Finance) categories.
Implied Volatility Functions
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Author : Veli-Matti Ahoranta
language : en
Publisher: LAP Lambert Academic Publishing
Release Date : 2010-12
Implied Volatility Functions written by Veli-Matti Ahoranta and has been published by LAP Lambert Academic Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-12 with categories.
Evidences that there are volatility smiles and smirks in various financial markets suggest that Black and Scholes (1973) valuation formula is not completely valid. This thesis investigates implied volatility patterns and -functions on Finnish warrant market. The intention of the thesis is to find answers to the three following questions: what is the form of the volatility structure in Finnish warrant markets? Does there exist a better method to estimate volatilities than basic Black-Scholes constant volatility model? In case that there exist a superior method to estimate volatilities, is the method constantly best with every level of moneyness and time to expiration? To find answers to these questions a sample data is gathered from the year 2006 and then it is analysed by using statistical measurements. The analysis provides interesting findings about the existence of volatility structures in Finnish markets and it provides interesting insights to the Finnish warrant markets
Implied Volatility Functions For One Factor And Two Factor Heath Jarrow And Morton Models
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Author : I-Doun Terry Kuo
language : en
Publisher:
Release Date : 2002
Implied Volatility Functions For One Factor And Two Factor Heath Jarrow And Morton Models written by I-Doun Terry Kuo and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with categories.
A Study Of The Implied Volatility Function
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Author : Qi Shi (M.Phil.)
language : en
Publisher:
Release Date : 2005
A Study Of The Implied Volatility Function written by Qi Shi (M.Phil.) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Options (Finance) categories.
Heath Jarrow And Morton Implied Volatility Functions And Conditional Heteroskedasticity Models
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Author : Kaushik I. Amin
language : en
Publisher:
Release Date : 1998
Heath Jarrow And Morton Implied Volatility Functions And Conditional Heteroskedasticity Models written by Kaushik I. Amin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with categories.
We evaluate various popular models of interest rate volatility and the Heath-Jarrow-Morton (HJM) approach to value interest rate derivatives by studying the information content and the forecast ability of HJM implied volatility in the Eurodollar futures options market. Implied volatility corresponding to the Ho-Lee, Courtadon, Cox-Ingersoll-Ross, Vasicek, and a linear proportional volatility model are examined within the HJM framework. The exercise compares these implied volatilities to a number of historical volatility benchmarks based on the GARCH model, the Glosten-Jagannathan-Runkle model, and several hybrid models combining the Cox-Ingersoll-Ross and Courtadon spot rate models and the GARCH and GJR approaches to model interest rate volatility. Our results show that there is a strong interaction effect between return shocks and the level of the interest rates in the volatility dynamics that none of the existing HJM volatility models and none of the GARCH type models can fully capture. Specifically, the impact of a shock to interest rate volatility is higher under a high interest rate than a low interest rate. The importance of implied volatility from the Ho-Lee, Courtadon, and Cox-Ingersoll-Ross models is significantly reduced after a term capturing the interaction effect is added to the volatility specification. The importance of implied volatility from the linear proportional and the Vasicek models is reduced but they can still explain a reasonably large portion of the time-variation in volatility.
Implied Adjusted Voladility Functions
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Author : Hanani Farhah binti Harun
language : en
Publisher:
Release Date : 2016
Implied Adjusted Voladility Functions written by Hanani Farhah binti Harun and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with categories.
Fitting Local Volatility Analytic And Numerical Approaches In Black Scholes And Local Variance Gamma Models
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Author : Andrey Itkin
language : en
Publisher: World Scientific
Release Date : 2020-01-22
Fitting Local Volatility Analytic And Numerical Approaches In Black Scholes And Local Variance Gamma Models written by Andrey Itkin and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-22 with Business & Economics categories.
The concept of local volatility as well as the local volatility model are one of the classical topics of mathematical finance. Although the existing literature is wide, there still exist various problems that have not drawn sufficient attention so far, for example: a) construction of analytical solutions of the Dupire equation for an arbitrary shape of the local volatility function; b) construction of parametric or non-parametric regression of the local volatility surface suitable for fast calibration; c) no-arbitrage interpolation and extrapolation of the local and implied volatility surfaces; d) extension of the local volatility concept beyond the Black-Scholes model, etc. Also, recent progresses in deep learning and artificial neural networks as applied to financial engineering have made it reasonable to look again at various classical problems of mathematical finance including that of building a no-arbitrage local/implied volatility surface and calibrating it to the option market data.This book was written with the purpose of presenting new results previously developed in a series of papers and explaining them consistently, starting from the general concept of Dupire, Derman and Kani and then concentrating on various extensions proposed by the author and his co-authors. This volume collects all the results in one place, and provides some typical examples of the problems that can be efficiently solved using the proposed methods. This also results in a faster calibration of the local and implied volatility surfaces as compared to standard approaches.The methods and solutions presented in this volume are new and recently published, and are accompanied by various additional comments and considerations. Since from the mathematical point of view, the level of details is closer to the applied rather than to the abstract or pure theoretical mathematics, the book could also be recommended to graduate students with majors in computational or quantitative finance, financial engineering or even applied mathematics. In particular, the author used to teach some topics of this book as a part of his special course on computational finance at the Tandon School of Engineering, New York University.
Does Net Buying Pressure Affect The Shape Of Implied Volatility Functions
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Author : Nicolas P. B. Bollen
language : en
Publisher:
Release Date : 2012
Does Net Buying Pressure Affect The Shape Of Implied Volatility Functions written by Nicolas P. B. Bollen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with categories.
This paper examines the relation between net buying pressure and the shape of the implied volatility function (IVF) of Samp;P 500 index options and options on twenty individual stocks. We find that time variation in the implied volatility of an option series is directly related to net buying pressure from public order flow. We also find that movements in implied volatility in the index option market are most strongly affected by buying pressure for index puts, while call options tend to dominate in stock option markets. Simulated delta-neutral trading strategies that sell options generate abnormal returns that match the deviations of the IVFs from historical volatility levels. Index option abnormal returns decrease monotonically across exercise prices and are significant, while stock option abnormal returns are symmetric, smaller, and insignificant. When vega risk is also hedged in the simulations using index options, however, the abnormal returns go from positive to negative, indicating that the steeply sloped IVF for index options does not present a profitable arbitrage opportunity once the costs of hedging have been considered.