Empirical Performance Of Option Pricing Models With Stochastic Local Volatility
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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.
Empirical Performance Of Alternative Option Pricing Models
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Author : Zhiwu Chen
language : en
Publisher:
Release Date : 2000
Empirical Performance Of Alternative Option Pricing Models written by Zhiwu Chen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with categories.
Substantial progress has been made in extending the Black-Scholes model to incorporate such features as stochastic volatility, stochastic interest rates and jumps.On the empirical front, however, it is not yet known whether and by how much each generalized feature will improve option pricing and hedging performance. This paper fills this gap by first developing an implementable option model in closed form that allows volatility, interest rates and jumps to bestochastic and that is parsimonious in the number of parameters. The model includes many known ones as special cases. Delta-neutral and single-instrument minimum-variance hedging strategies are derived analytically. Using Samp;P 500 options, we examine a set of alternative models from three perspectives: (1) internal consistency of implied parameters/volatility with relevant time-series data, (2)out-of-sample pricing and (3) hedging performance. The models of focus include the benchmark Black-Scholes formula and the ones that respectively allow for (i) stochastic volatility, (ii) both stochastic volatility and stochastic interest rates, and (iii) stochastic volatility and jumps.Overall, incorporating both stochastic volatility and random jumps produces the best pricing performance and the most internally-consistent implied-volatility process. Its implied volatility does not quot;smilequot; across moneyness. But, for hedging, adding either jumps or stochastic interest rates does not seem to improve performance any further once stochastic volatility is taken into account.
Empirical Performance Study Of Alternative Option Pricing Models
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Author : Sofiane Aboura
language : en
Publisher:
Release Date : 2015
Empirical Performance Study Of Alternative Option Pricing Models written by Sofiane Aboura and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with categories.
The mispricing of the deep-in-the money and deep-out-the-money generated by the Black-Scholes (1973) model is now well documented in the literature. In this paper, we discuss different option valuation models on the basis of empirical tests carry out on the French option market. We examine methods that account for non-normal skewness and kurtosis, relax the martingale restriction, mix two log-normal distributions, and allows either for jump diffusion process or for stochastic volatility. We find that the use of a jump diffusion and stochastic volatility model performs as well as the inclusion of non normal skewness and kurtosis in terms of precision in the option valuation.Keywords : Implied Volatility, Stochastic Volatility Model, Jump Diffusion Model, Skewness, Kurtosis.
An Empirical Comparison Of Alternative Stochastic Volatility Option Pricing Models
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Author : Tiezhu Gao
language : en
Publisher:
Release Date : 2006
An Empirical Comparison Of Alternative Stochastic Volatility Option Pricing Models written by Tiezhu Gao 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.
A Time Series Approach To Option Pricing
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Author : Christophe Chorro
language : en
Publisher: Springer
Release Date : 2014-12-04
A Time Series Approach To Option Pricing written by Christophe Chorro and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-04 with Business & Economics categories.
The current world financial scene indicates at an intertwined and interdependent relationship between financial market activity and economic health. This book explains how the economic messages delivered by the dynamic evolution of financial asset returns are strongly related to option prices. The Black Scholes framework is introduced and by underlining its shortcomings, an alternative approach is presented that has emerged over the past ten years of academic research, an approach that is much more grounded on a realistic statistical analysis of data rather than on ad hoc tractable continuous time option pricing models. The reader then learns what it takes to understand and implement these option pricing models based on time series analysis in a self-contained way. The discussion covers modeling choices available to the quantitative analyst, as well as the tools to decide upon a particular model based on the historical datasets of financial returns. The reader is then guided into numerical deduction of option prices from these models and illustrations with real examples are used to reflect the accuracy of the approach using datasets of options on equity indices.
Essays On American Options Pricing Under Levy Models With Stochastic Volatility And Jumps
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Author : Ye Chen
language : en
Publisher:
Release Date : 2019
Essays On American Options Pricing Under Levy Models With Stochastic Volatility And Jumps written by Ye Chen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with categories.
In ``A Multi-demensional Transform for Pricing American Options Under Stochastic Volatility Models", we present a new transform-based approach for pricing American options under low-dimensional stochastic volatility models which can be used to construct multi-dimensional path-independent lattices for all low-dimensional stochastic volatility models given in the literature, including SV, SV2, SVJ, SV2J, and SVJ2 models. We demonstrate that the prices of European options obtained using the path-independent lattices converge rapidly to their true prices obtained using quasi-analytical solutions. Our transform-based approach is computationally more efficient than all other methods given in the literature for a large class of low-dimensional stochastic volatility models. In ``A Multi-demensional Transform for Pricing American Options Under Levy Models", We extend the multi-dimensional transform to Levy models with stochastic volatility and jumps in the underlying stock price process. Efficient path-independent tree can be constructed for both European and American options. Our path-independent lattice method can be applied to almost all Levy models in the literature, such as Merton (1976), Bates (1996, 2000, 2006), Pan (2002), the NIG model, the VG model and the CGMY model. The numerical results show that our method is extemly accurate and fast. In ``Empirical performance of Levy models for American Options", we investigate in-sample fitting and out-of-sample pricing performance on American call options under Levy models. The drawback of the BS model has been well documented in the literatures, such as negative skewness with excess kurtosis, fat tail, and non-normality. Therefore, many models have been proposed to resolve known issues associated the BS model. For example, to resolve volatility smile, local volatility, stochastic volatility, and diffusion with jumps have been considered in the literatures; to resolve non-normality, non-Markov processes have been considered, e.g., Poisson process, variance gamma process, and other type of Levy processes. One would ask: what is the gain from each of the generalized models? Or, which model is the best for option pricing? We address these problems by examining which model results in the lowest pricing error for American style contracts. For in-sample analysis, the rank (from best to worst) is Pan, CGMYsv, VGsv, Heston, CGMY, VG and BS. And for out-of-sample pricing performance, the rank (from best to worst) is CGMYsv, VGsv, Pan, Heston, BS, VG, and CGMY. Adding stochastic volatility and jump into a model improves American options pricing performance, but pure jump models are worse than the BS model in American options pricing. Our empirical results show that pure jump model are over-fitting, but not improve American options pricing when they are applied to out-of-sample data.
The Hybrid Stochastic Local Volatility Model With Applications In Pricing Fx Options
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Author : Yu Tian
language : en
Publisher:
Release Date : 2016
The Hybrid Stochastic Local Volatility Model With Applications In Pricing Fx Options written by Yu Tian 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.
This thesis presents our study on using the hybrid stochastic-local volatility model for option pricing. Many researchers have demonstrated that stochastic volatility models cannot capture the whole volatility surface accurately, although the model parameters have been calibrated to replicate the market implied volatility data for near at-the-money strikes. On the other hand, the local volatility model can reproduce the implied volatility surface, whereas it does not consider the stochastic behaviour of the volatility. To combine the advantages of stochastic volatility (SV) and local volatility (LV) models, a class of stochastic-local volatility (SLV) models has been developed. The SLV model contains a stochastic volatility component represented by a volatility process and a local volatility component represented by a so-called leverage function. The leverage function can be roughly seen as a ratio between local volatility and conditional expectation of stochastic volatility. The difficulty of implementing the SLV model lies in the calibration of the leverage function. In the thesis, we first review the fundamental theories of stochastic differential equations and the classic option pricing models, and study the behaviour of the volatility in the context of FX market. We then introduce the SLV model and illustrate our implementation of the calibration and pricing procedure. We apply the SLV model to exotic option pricing in the FX market and compare pricing results of the SLV model with pure local volatility and pure stochastic volatility models. Numerical results show that the SLV model can match the implied volatility surface very well as well as improve the pricing performance for barrier options. In addition, we further discuss some extensions of the SLV project, such as parallelization potential for accelerating option pricing and pricing techniques for window barrier options. Although the SLV model we use in the thesis is not entirely new, we contribute to the research in the following aspects: 1) we investigate the hybrid volatility modeling thoroughly from theoretical backgrounds to practical implementations; 2) we resolve some critical issues in implementing the SLV model such as developing a fast and stable numerical method to derive the leverage function; and 3) we build a robust calibration and pricing platform under the SLV model, which can be extended for practical uses.
A Theoretical And Empirical Evaluation Of The Performance Of Option Pricing Models Under Stochastic Volatility
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Author :
language : en
Publisher:
Release Date : 2016
A Theoretical And Empirical Evaluation Of The Performance Of Option Pricing Models Under Stochastic Volatility written by 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.
Application Of Stochastic Volatility Models In Option Pricing
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Author : Pascal Debus
language : de
Publisher: GRIN Verlag
Release Date : 2013-09-09
Application Of Stochastic Volatility Models In Option Pricing written by Pascal Debus and has been published by GRIN Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09-09 with Business & Economics categories.
Bachelorarbeit aus dem Jahr 2010 im Fachbereich BWL - Investition und Finanzierung, Note: 1,2, EBS Universität für Wirtschaft und Recht, Sprache: Deutsch, Abstract: The Black-Scholes (or Black-Scholes-Merton) Model has become the standard model for the pricing of options and can surely be seen as one of the main reasons for the growth of the derivative market after the model ́s introduction in 1973. As a consequence, the inventors of the model, Robert Merton, Myron Scholes, and without doubt also Fischer Black, if he had not died in 1995, were awarded the Nobel prize for economics in 1997. The model, however, makes some strict assumptions that must hold true for accurate pricing of an option. The most important one is constant volatility, whereas empirical evidence shows that volatility is heteroscedastic. This leads to increased mispricing of options especially in the case of out of the money options as well as to a phenomenon known as volatility smile. As a consequence, researchers introduced various approaches to expand the model by allowing the volatility to be non-constant and to follow a sto-chastic process. It is the objective of this thesis to investigate if the pricing accuracy of the Black-Scholes model can be significantly improved by applying a stochastic volatility model.
Volatility Surface And Term Structure
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Author : Kin Keung Lai
language : en
Publisher: Routledge
Release Date : 2013-09-11
Volatility Surface And Term Structure written by Kin Keung Lai and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09-11 with Business & Economics categories.
This book provides different financial models based on options to predict underlying asset price and design the risk hedging strategies. Authors of the book have made theoretical innovation to these models to enable the models to be applicable to real market. The book also introduces risk management and hedging strategies based on different criterions. These strategies provide practical guide for real option trading. This book studies the classical stochastic volatility and deterministic volatility models. For the former, the classical Heston model is integrated with volatility term structure. The correlation of Heston model is considered to be variable. For the latter, the local volatility model is improved from experience of financial practice. The improved local volatility surface is then used for price forecasting. VaR and CVaR are employed as standard criterions for risk management. The options trading strategies are also designed combining different types of options and they have been proven to be profitable in real market. This book is a combination of theory and practice. Users will find the applications of these financial models in real market to be effective and efficient.