Relative Pricing Of Options With Stochastic Volatility
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Relative Pricing Of Options With Stochastic Volatility
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Author : Olivier Ledoit
language : en
Publisher:
Release Date : 1998
Relative Pricing Of Options With Stochastic Volatility written by Olivier Ledoit 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.
This paper offers a new approach for pricing options on assets with stochastic volatility. We start by constructing the quot;surfacequot; of Black-Scholes implied volatilities for (readily observable) liquid, European call options with varying strike prices and maturities. Then, we show that the implied volatility of an at-the-money call option with time-to-maturity going tozero is equal to the underlying asset's instantaneous (stochastic) volatility. We then model the stochastic processes followed by the implied volatilities of options of all maturities and strike prices jointly with the stock price, and find a no-arbitrage condition that their drift must satisfy. Finally, we use the resulting arbitrage-free joint process for the stock price and its volatility to price other derivatives, such as standard but illiquid options as well as exotic options using numerical methods. The great advantage of our approach is that, when pricing these other derivatives, we are secure in the knowledge that the model values the hedging instruments - namely the stock and the simple, liquid options - consistently with the market. Our approach can easily be extended to allow for stochastic interest rates and a stochastic dividend yield, which may be particularly relevant to the pricing of currency and commodity options. We can also extend our model to price bond options when the term structure of interest rates has stochastic volatility.
A Simple New Formula For Options With Stochastic Volatility
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Author : Steven L. Heston
language : en
Publisher:
Release Date : 1998
A Simple New Formula For Options With Stochastic Volatility written by Steven L. Heston 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.
This paper shows a relationship between bond pricing models and option pricing models with stochastic volatility. It exploits this relationship to find a new stochastic volatility model with a closed-form solution for European option prices. The model allows nonzero correlation between volatility and spot asset returns. When the correlation is unity the model contains the Black-Scholes [1973] model and Cox's [1975] constant elasticity of variance model as special cases. The option formula preserves the Black-Scholes property that changes in volatility are equivalent to changes in option expiration.
Empirical Performance Of Option Pricing Models With Stochastic Local Volatility
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Author : Greg Orosi
language : en
Publisher:
Release Date : 2014
Empirical Performance Of Option Pricing Models With Stochastic Local Volatility written by Greg Orosi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with categories.
We examine the empirical performance of several stochastic local volatility models that are the extensions of the Heston stochastic volatility model. Our results indicate that the stochastic volatility model with quadratic local volatility significantly outperforms the stochastic volatility model with CEV type local volatility. Moreover, we compare the performance of these models to several other benchmarks and find that the quadratic local volatility model compares well to the best performing option pricing models reported in the current literature for European-style S&P500 index options. Our results also indicate that the model with quadratic local volatility reproduces the characteristics of the implied volatility surface more accurately than the Heston model. Finally, we demonstrate that capturing the shape of the implied volatility surface is necessary to price binary options accurately.
Spanned Stochastic Volatility In Bond Markets
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Author : Don H. Kim
language : en
Publisher:
Release Date : 2007
Spanned Stochastic Volatility In Bond Markets written by Don H. Kim and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with 1996-2008 categories.
This paper reexamines the issue of unspanned stochastic volatility (USV) in bond markets and the puzzle of poor relative pricing between bonds and bond options. I make a distinction between the "weak USV" and the "strong USV" scenarios, and analyze the evidence for each of them. I argue that the poor bonds/options relative pricing in the extant literature is not necessarily evidence for the strong USV scenario, and show that a maximally flexible 2-factor quadratic-Gaussian model (a non-USV model) estimated without bond options data can capture much of the movement in bond option prices. Dropping the positive-definiteness requirement for nominal interest rates and adopting "regularized" estimations turn out to be important for obtaining sensible results.
Option Valuation Under Stochastic Volatility
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Author : Alan L. Lewis
language : en
Publisher:
Release Date : 2000
Option Valuation Under Stochastic Volatility written by Alan L. Lewis and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Business & Economics categories.
On Stochastic Dominance Optionbounds In Discrete And Continuous Space And Time With Stochastic And Deterministic Volatility And Pricing With Constant Relative Risk Aversion
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Author : Eli Rose
language : en
Publisher:
Release Date : 2020
On Stochastic Dominance Optionbounds In Discrete And Continuous Space And Time With Stochastic And Deterministic Volatility And Pricing With Constant Relative Risk Aversion written by Eli Rose and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with Business mathematics categories.
This thesis makes original contributions to the field of asset pricing, which is a field dedicated to describing the prices of financial instruments and their characteristics. The prices of these financial instruments are determined by the behavior of investors who buy and sell them, and so asset pricing is ultimately done by modeling the behavior of investors. One method for achieving this is through the framework of stochastic dominance. This thesis specifically deals with a specific class of financial instruments called European options and reviews the literature on stochastic dominance option pricing and discusses new methods for finding stochastic dominance bounds on options in both discrete and continuous time under both deterministic and stochastic volatility. The results presented here extends the works of Ritchken and Kuo (1988) and Perrakis and Ryan (1984). Furthermore, stochastic dominance bounds for Heston's (1993) stochastic volatility model are obtained under certain assumptions. Finally, this thesis extends the work of Carr and Madan (1999) and solves for the characteristic function of the call price given the physical characteristic function under the CRRA utility model.
Index Option Pricing With Stochastic Volatility And The Value Of Accurate Variance Forecasts
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Author : Robert F. Engle
language : en
Publisher:
Release Date : 1993
Index Option Pricing With Stochastic Volatility And The Value Of Accurate Variance Forecasts written by Robert F. Engle and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Stock options categories.
In pricing primary-market options and in making secondary markets, financial intermediaries depend on the quality of forecasts of the variance of the underlying assets. Hence, the gain from improved pricing of options would be a measure of the value of a forecast of underlying asset returns. NYSE index returns over the period of 1968-1991 are used to suggest that pricing index options of up to 90-days maturity would be more accurate when: (1) using ARCH specifications in place of a moving average of squared returns; (2) using Hull and White's (1987) adjustment for stochastic variance in Black and Scholes's (1973) formula; (3) accounting explicitly for weekends and the slowdown of variance whenever the market is closed.
Option Pricing Under Stochastic Volatility
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Author : Dimitrios Gkamas
language : en
Publisher:
Release Date : 2002
Option Pricing Under Stochastic Volatility written by Dimitrios Gkamas 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.
Stochastic Volatility In Mean Option Pricing Models
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Author : Lishan Shi
language : en
Publisher:
Release Date : 2006
Stochastic Volatility In Mean Option Pricing Models written by Lishan Shi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with categories.
Stochastic Volatility Option Pricing
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Author : Spiridon Floratos
language : en
Publisher:
Release Date : 2004
Stochastic Volatility Option Pricing written by Spiridon Floratos and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with categories.