An Analytical Approximation For European Option Prices Under Stochastic Interest Rate Economy
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An Analytical Approximation For European Option Prices Under Stochastic Interest Rate Economy
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Author : Hideharu Funahashi
language : en
Publisher:
Release Date : 2015
An Analytical Approximation For European Option Prices Under Stochastic Interest Rate Economy written by Hideharu Funahashi 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.
This paper extends the Wiener-Ito chaos expansion approach proposed by Funahashi and Kijima (2013) to an equity-interest-rate hybrid model for the pricing of European contingent claims with special emphasis on calibration to the option markets. Our model can capture the volatility skew and smile of option markets, as well as the stochastic nature of interest rates. Further, the proposed method is applicable to widely used option pricing models such as local volatility models, stochastic volatility models, and their combinations with the stochastic nature of interest rates; hence, it is suitable for practical purposes. Through numerical examples, we show that our approximation is quite accurate even for long-maturity and/or high-volatility cases.
An Investigation Of The Impact Of Stochastic Interest Rates On The Pricing Of Equity Options
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Author : Peter Carayannopoulos
language : en
Publisher:
Release Date : 1993
An Investigation Of The Impact Of Stochastic Interest Rates On The Pricing Of Equity Options written by Peter Carayannopoulos and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with categories.
Pde And Martingale Methods In Option Pricing
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Author : Andrea Pascucci
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-04-15
Pde And Martingale Methods In Option Pricing written by Andrea Pascucci and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-04-15 with Mathematics categories.
This book offers an introduction to the mathematical, probabilistic and numerical methods used in the modern theory of option pricing. The text is designed for readers with a basic mathematical background. The first part contains a presentation of the arbitrage theory in discrete time. In the second part, the theories of stochastic calculus and parabolic PDEs are developed in detail and the classical arbitrage theory is analyzed in a Markovian setting by means of of PDEs techniques. After the martingale representation theorems and the Girsanov theory have been presented, arbitrage pricing is revisited in the martingale theory optics. General tools from PDE and martingale theories are also used in the analysis of volatility modeling. The book also contains an Introduction to Lévy processes and Malliavin calculus. The last part is devoted to the description of the numerical methods used in option pricing: Monte Carlo, binomial trees, finite differences and Fourier transform.
Option Prices In Stochastic Volatility Models
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Author : Giulia Terenzi
language : en
Publisher:
Release Date : 2018
Option Prices In Stochastic Volatility Models written by Giulia Terenzi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with categories.
We study option pricing problems in stochastic volatility models. In the first part of this thesis we focus on American options in the Heston model. We first give an analytical characterization of the value function of an American option as the unique solution of the associated (degenerate) parabolic obstacle problem. Our approach is based on variational inequalities in suitable weighted Sobolev spaces and extends recent results of Daskalopoulos and Feehan (2011, 2016) and Feehan and Pop (2015). We also investigate the properties of the American value function. In particular, we prove that, under suitable assumptions on the payoff, the value function is nondecreasing with respect to the volatility variable. Then, we focus on an American put option and we extend some results which are well known in the Black and Scholes world. In particular, we prove the strict convexity of the value function in the continuation region, some properties of the free boundary function, the Early Exercise Price formula and a weak form of the smooth fit principle. This is done mostly by using probabilistic techniques.In the second part we deal with the numerical computation of European and American option prices in jump-diffusion stochastic volatility models. We first focus on the Bates-Hull-White model, i.e. the Bates model with a stochastic interest rate. We consider a backward hybrid algorithm which uses a Markov chain approximation (in particular, a “multiple jumps” tree) in the direction of the volatility and the interest rate and a (deterministic) finite-difference approach in order to handle the underlying asset price process. Moreover, we provide a simulation scheme to be used for Monte Carlo evaluations. Numerical results show the reliability and the efficiency of the proposed methods.Finally, we analyze the rate of convergence of the hybrid algorithm applied to general jump-diffusion models. We study first order weak convergence of Markov chains to diffusions under quite general assumptions. Then, we prove the convergence of the algorithm, by studying the stability and the consistency of the hybrid scheme, in a sense that allows us to exploit the probabilistic features of the Markov chain approximation.
The Art Of Quantitative Finance Vol 2
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Author : Gerhard Larcher
language : en
Publisher: Springer Nature
Release Date : 2023-03-23
The Art Of Quantitative Finance Vol 2 written by Gerhard Larcher and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-23 with Business & Economics categories.
This textbook provides the necessary techniques from financial mathematics and stochastic analysis for the valuation of more complex financial products and strategies. The author discusses how to make use of mathematical methods to analyse volatilities in capital markets. Furthermore, he illustrates how to apply and extend the Black-Scholes theory to several fields in finance. In the final section of the book, the author introduces the readers to the fundamentals of stochastic analysis and presents examples of applications. This book builds on the previous volume of the author’s trilogy on quantitative finance. The aim of the second volume is to present and discuss more complex and advanced techniques of modern financial mathematics in a way that is intuitive and easy to follow. As in the previous volume, the author provides financial mathematicians with insights into practical requirements when applying financial mathematical techniques in the real world.
Option Pricing Under Stochastic Volatility And Stochastic Interest Rate In The Spanish Case
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Author : Marc Sáez
language : en
Publisher:
Release Date : 1995
Option Pricing Under Stochastic Volatility And Stochastic Interest Rate In The Spanish Case written by Marc Sáez and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Options (Finance) 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.
Option Pricing Under Stochastic Volatility And Stochastic Interest Rate In The Spanish Case
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Author : Marc Sáez i Zafra
language : en
Publisher:
Release Date : 1995
Option Pricing Under Stochastic Volatility And Stochastic Interest Rate In The Spanish Case written by Marc Sáez i Zafra and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with categories.
S Ganesan Justin Paul
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Author :
language : en
Publisher: Allied Publishers
Release Date :
S Ganesan Justin Paul written by and has been published by Allied Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Analytical Approximations Of Option Prices In Stochastic Volatility Models
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Author :
language : en
Publisher:
Release Date : 2007
Analytical Approximations Of Option Prices In Stochastic Volatility Models written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with categories.