Markov Chains And The Pricing For Derivatives
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Author | : Harry Chung Heng Lo |
Publisher | : |
Total Pages | : 252 |
Release | : 2009 |
Genre | : |
ISBN | : |
A numerical method for pricing financial derivatives based on continuous-time Markov chains is proposed. It approximates the underlying stochastic process by continuous-time Markov chain. We show how to construct a multi-dimensional continuous-time Markov chain such that it converges in distribution to a multi-dimensional diffusion process. The method is flexible enough to be applied to a model where the underlying process contains local volatility, stochastic volatility and jumps (both finite and infinite activity). Ferthermore, we introduce a method to approximate the dynamics of the realized variance of Markov Chain and an algorithm to reduce the complexity of computing the joint probability distribution between the realized variance and the underlying.
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Release | : 2012 |
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Author | : Sanjiv Ranjan Das |
Publisher | : |
Total Pages | : |
Release | : 2009 |
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ISBN | : |
Derivative security pricing and risk measurement relies increasingly on lattice representations of stochastic processes, which are a discrete approximation of the movement of the underlying securities. Pricing is undertaken by summation of node values on the lattice. When the lattice is large (which is the case when high accuracy is required), exhaustive enumeration of the nodes becomes prohibitively costly. Instead, Monte Carlo simulation is used to estimate the lattice value by sampling appropriately from the nodes. Most sampling methods become extremely error-prone in situations where the node values vary widely. This paper presents a Markov chain Monte Carlo scheme, adapted from Sinclair and Jerrum (Information and Computation 82 (1989)), that is able to overcome this problem, provided some partial (possibly very inaccurate) information about the lattice sum is available. This partial information is used to direct the sampling, in similar fashion to traditional importance sampling methods. The key difference is that the algorithm allows backtracking on the lattice, which acts in a quot;self-correctingquot; manner to minimize the bias in the importance sampling.
Author | : Chia Lo |
Publisher | : |
Total Pages | : 43 |
Release | : 2014 |
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We propose a non-equidistant Q rate matrix setting formula such that a well-defined continuous time Markov chain can lead to excellent approximations to jump-diffusions with affine or non-affine functional specifications. This approach also accommodates state-dependent jump intensity and jump distribution, a fexibility that is very hard to achieve with traditional numerical methods. Our approach not only satisfies Kushner (1990) local consistency conditions but also resolves the approximation errors induced by Piccioni (1987) scheme. European stock option pricing examples based on jump-diffusions illustrate the ease of implementation of our model. The proposed algorithm for pricing American options highlights the speed and accuracy. Finally the empirical analysis using daily VIX data shows that the maximum likelihood estimates of the underlying jump-diffusions can be efficiently computed by the model proposed in this article.
Author | : Zhenyu Cui |
Publisher | : |
Total Pages | : 32 |
Release | : 2019 |
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ISBN | : |
In this chapter, we present recent developments in using the tools of continuous-time Markov chains for the valuation of European and path-dependent financial derivatives. We also survey results on a newly proposed regime switching approximation to stochastic volatility, and stochastic local volatility models. The presented framework is part of an exciting recent stream of literature on numerical option pricing, and offers a new perspective that combines the theory of diffusion processes, Markov chains, and Fourier techniques. It is also elegantly connected to partial differential equation (PDE) approaches.
Author | : Michael A. H. Dempster |
Publisher | : Cambridge University Press |
Total Pages | : 614 |
Release | : 1997-10-13 |
Genre | : Business & Economics |
ISBN | : 9780521584241 |
During 1995 the Isaac Newton Institute for the Mathematical Sciences at Cambridge University hosted a six month research program on financial mathematics. During this period more than 300 scholars and financial practitioners attended to conduct research and to attend more than 150 research seminars. Many of the presented papers were on the subject of financial derivatives. The very best were selected to appear in this volume. They range from abstract financial theory to practical issues pertaining to the pricing and hedging of interest rate derivatives and exotic options in the market place. Hence this book will be of interest to both academic scholars and financial engineers.
Author | : Thomas Wake Epps |
Publisher | : World Scientific Publishing Company |
Total Pages | : 644 |
Release | : 2007-06-04 |
Genre | : Business & Economics |
ISBN | : 9814365432 |
This book presents techniques for valuing derivative securities at a level suitable for practitioners, students in doctoral programs in economics and finance, and those in masters-level programs in financial mathematics and computational finance. It provides the necessary mathematical tools from analysis, probability theory, the theory of stochastic processes, and stochastic calculus, making extensive use of examples. It also covers pricing theory, with emphasis on martingale methods. The chapters are organized around the assumptions made about the dynamics of underlying price processes. Readers begin with simple, discrete-time models that require little mathematical sophistication, proceed to the basic Black-Scholes theory, and then advance to continuous-time models with multiple risk sources. The second edition takes account of the major developments in the field since 2000. New topics include the use of simulation to price American-style derivatives, a new one-step approach to pricing options by inverting characteristic functions, and models that allow jumps in volatility and Markov-driven changes in regime. The new chapter on interest-rate derivatives includes extensive coverage of the LIBOR market model and an introduction to the modeling of credit risk. As a supplement to the text, the book contains an accompanying CD-ROM with user-friendly FORTRAN, C++, and VBA program components.
Author | : Nicholas H. Bingham |
Publisher | : Springer Science & Business Media |
Total Pages | : 447 |
Release | : 2013-06-29 |
Genre | : Mathematics |
ISBN | : 1447138562 |
This second edition - completely up to date with new exercises - provides a comprehensive and self-contained treatment of the probabilistic theory behind the risk-neutral valuation principle and its application to the pricing and hedging of financial derivatives. On the probabilistic side, both discrete- and continuous-time stochastic processes are treated, with special emphasis on martingale theory, stochastic integration and change-of-measure techniques. Based on firm probabilistic foundations, general properties of discrete- and continuous-time financial market models are discussed.
Author | : Valentina Prezioso |
Publisher | : |
Total Pages | : |
Release | : 2010* |
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Author | : Antoine Petrus Cornelius van der Ploeg |
Publisher | : Rozenberg Publishers |
Total Pages | : 358 |
Release | : 2006 |
Genre | : |
ISBN | : 9051705778 |