Stochastic Volatility Option Pricing In Discrete Time

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Stochastic Volatility Option Pricing In Discrete Time

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Author : Victor K. Ng
language : en
Publisher:
Release Date : 1991

Stochastic Volatility Option Pricing In Discrete Time written by Victor K. Ng and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Options (Finance) categories.

Introduction To Option Pricing Theory

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Author : Gopinath Kallianpur
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Introduction To Option Pricing Theory written by Gopinath Kallianpur 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 2012-12-06 with Mathematics categories.

Since the appearance of seminal works by R. Merton, and F. Black and M. Scholes, stochastic processes have assumed an increasingly important role in the development of the mathematical theory of finance. This work examines, in some detail, that part of stochastic finance pertaining to option pricing theory. Thus the exposition is confined to areas of stochastic finance that are relevant to the theory, omitting such topics as futures and term-structure. This self-contained work begins with five introductory chapters on stochastic analysis, making it accessible to readers with little or no prior knowledge of stochastic processes or stochastic analysis. These chapters cover the essentials of Ito's theory of stochastic integration, integration with respect to semimartingales, Girsanov's Theorem, and a brief introduction to stochastic differential equations. Subsequent chapters treat more specialized topics, including option pricing in discrete time, continuous time trading, arbitrage, complete markets, European options (Black and Scholes Theory), American options, Russian options, discrete approximations, and asset pricing with stochastic volatility. In several chapters, new results are presented. A unique feature of the book is its emphasis on arbitrage, in particular, the relationship between arbitrage and equivalent martingale measures (EMM), and the derivation of necessary and sufficient conditions for no arbitrage (NA). {\it Introduction to Option Pricing Theory} is intended for students and researchers in statistics, applied mathematics, business, or economics, who have a background in measure theory and have completed probability theory at the intermediate level. The work lends itself to self-study, as well as to a one-semester course at the graduate level.

Vix Computation Based On Affine Stochastic Volatility Models In Discrete Time

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Author : Asmerilda Hitaj
language : en
Publisher:
Release Date : 2015

Vix Computation Based On Affine Stochastic Volatility Models In Discrete Time written by Asmerilda Hitaj 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.

We propose a class of discrete-time stochastic volatility models that, in a parsimonious way, captures the time-varying higher moments observed in financial series. We build this class of models in order to reach two desirable results. Firstly, we have a recursive procedure for the characteristic function of the log price at maturity that allows a semi-analytical formula for option prices as in Heston and Nandi (2000). Secondly, we try to reproduce some features of the VIX Index. We derive a simple formula for the VIX index and use it for option pricing purposes.

Stochastic Dominance And Option Pricing In Discrete And Continuous Time

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Author : Ioan Mihai Oancea
language : en
Publisher:
Release Date : 2007

Stochastic Dominance And Option Pricing In Discrete And Continuous Time written by Ioan Mihai Oancea 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.

This paper examines option pricing in a universe in which it is assumed that markets are incomplete. It derives multiperiod discrete time option bounds based on stochastic dominance considerations for a risk-averse investor holding only the underlying asset, the riskless asset and (possibly) the option for any type of underlying asset distribution, discrete or continuous. It then considers the limit behavior of these bounds for special categories of such distributions as trading becomes progressively more dense, tending to continuous time. It is shown that these bounds nest as special cases most, if not all, existing arbitrage- and equilibrium-based option pricing models. Thus, when the underlying asset follows a generalized diffusion both bounds converge to a single value. For jump-diffusion processes, stochastic volatility models, and GARCH processes the bounds remain distinct and define several new option pricing results containing as special cases the arbitrage-based results.

Discrete Time Stochastic Volatility

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Author : Thomas Roos
language : en
Publisher:
Release Date : 2017

Discrete Time Stochastic Volatility written by Thomas Roos and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with categories.

We propose a new methodology for obtaining arbitrage free European option prices from a SABR-like parameterisation. The method consists of specifying the joint distribution of the volatility and underlying at a given expiry and requires the calculation of a simple one-dimensional numerical integral per option price. CMS prices and some more general payouts can also be obtained as one-dimensional integrals. The specification of the volatility function is flexible and allows additional control over the wings of the distribution. The approach itself is general and applicable to a variety of asset classes.

A Stochastic Volatility Model With Realized Measures For Option Pricing

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Author : Giacomo Bormetti
language : en
Publisher:
Release Date : 2019

A Stochastic Volatility Model With Realized Measures For Option Pricing written by Giacomo Bormetti 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.

Based on the fact that realized measures of volatility are affected by measurement errors, we introduce a new family of discrete-time stochastic volatility models having two measurement equations relating both observed returns and realized measures to the latent conditional variance. A semi-analytical option pricing framework is developed for this class of models. In addition, we provide analytical filtering and smoothing recursions for the basic specification of the model, and an effective MCMC algorithm for its richer variants. The empirical analysis shows the effectiveness of filtering and smoothing realized measures in inflating the latent volatility persistence - the crucial parameter in pricing Standard and Poor's 500 Index options.

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.

Stochastic Volatility Long Term Option And Discrete Time Problems In Fx

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Author : Francois-Stephane Robert Mantion
language : en
Publisher:
Release Date : 1998

Stochastic Volatility Long Term Option And Discrete Time Problems In Fx written by Francois-Stephane Robert Mantion 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.

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.

Two Problems On Option Pricing

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Author : Stefano Herzel
language : en
Publisher:
Release Date : 1997

Two Problems On Option Pricing written by Stefano Herzel and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with categories.