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Download or read book Forward and Inverse American Option Pricing Via a Complementarity Approach written by and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Carl Chiarella
Publisher : World Scientific
ISBN 13 : 9814452629
Total Pages : 223 pages
Book Rating : 4.8/5 (144 download)
Download or read book The Numerical Solution of the American Option Pricing Problem written by Carl Chiarella and published by World Scientific. This book was released on 2014-10-14 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: The early exercise opportunity of an American option makes it challenging to price and an array of approaches have been proposed in the vast literature on this topic. In The Numerical Solution of the American Option Pricing Problem, Carl Chiarella, Boda Kang and Gunter Meyer focus on two numerical approaches that have proved useful for finding all prices, hedge ratios and early exercise boundaries of an American option. One is a finite difference approach which is based on the numerical solution of the partial differential equations with the free boundary problem arising in American option pricing, including the method of lines, the component wise splitting and the finite difference with PSOR. The other approach is the integral transform approach which includes Fourier or Fourier Cosine transforms. Written in a concise and systematic manner, Chiarella, Kang and Meyer explain and demonstrate the advantages and limitations of each of them based on their and their co-workers'' experiences with these approaches over the years. Contents: Introduction; The Merton and Heston Model for a Call; American Call Options under Jump-Diffusion Processes; American Option Prices under Stochastic Volatility and Jump-Diffusion Dynamics OCo The Transform Approach; Representation and Numerical Approximation of American Option Prices under Heston; Fourier Cosine Expansion Approach; A Numerical Approach to Pricing American Call Options under SVJD; Conclusion; Bibliography; Index; About the Authors. Readership: Post-graduates/ Researchers in finance and applied mathematics with interest in numerical methods for American option pricing; mathematicians/physicists doing applied research in option pricing. Key Features: Complete discussion of different numerical methods for American options; Able to handle stochastic volatility and/or jump diffusion dynamics; Able to produce hedge ratios efficiently and accurately"
Author : Liang Tan
Publisher : LAP Lambert Academic Publishing
ISBN 13 : 9783838304427
Total Pages : 176 pages
Book Rating : 4.3/5 (44 download)
Download or read book Numerical Evaluation of American Options written by Liang Tan and published by LAP Lambert Academic Publishing. This book was released on 2009-11 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book we discuss various numerical evaluation problems for American options. Base on Black-Scholes framework, we establish partial differential complementarity problems (PDCP) for American options. Then we introduced various finite difference schemes to discretize the PDCP to obtain a system of Linear Complementarity Problems. The solution analysis and numerical algorithms are discussed. Next we study the pricing problem for American options whose payoff function are determined by two or more underlying assets. We formulate the two-asset American option pricing problem as two-dimensional PDCP. We first perform some state variable transformation and then introduce the ADI scheme and LOD scheme. After this, we discuss American option on an underlying asset with stochastic volatility. At last we consider the implied volatility problem for American options. We formulate a mathematical program with complementarity constraints (MPCC). Then we applied a penalty approach to solve the MPCC by utilizing the existing NLP tools. The parameter estimation problem for a mean-reverting stochastic volatility process is also considered.
Author : Tapiwa Maswera
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (135 download)
Download or read book Fixed Point Iterative Methods for Linear Complementarity Problems in American Option Pricing written by Tapiwa Maswera and published by . This book was released on 2017 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The linear complementarity formulation for American option pricing is studied. In particular, fixed point solution methods from literature are considered. Here simplified proofs for convergence criterion are provided. Further generalizations and modifications are also suggested alongside more tractable convergence analysis. Alternative formulations for the option pricing problem are also surveyed. These will be in the form of the Chapman-Kolmogorov lattice methods and the Modified Mellin transform framework. Some numerical experiments are then conducted for comparison purposes.
Author : Lishang Jiang
Publisher : World Scientific
ISBN 13 : 9812563695
Total Pages : 344 pages
Book Rating : 4.8/5 (125 download)
Download or read book Mathematical Modeling and Methods of Option Pricing written by Lishang Jiang and published by World Scientific. This book was released on 2005 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the perspective of partial differential equations (PDE), this book introduces the Black-Scholes-Merton's option pricing theory. A unified approach is used to model various types of option pricing as PDE problems, to derive pricing formulas as their solutions, and to design efficient algorithms from the numerical calculation of PDEs.
Author : Jerome Detemple
Publisher : CRC Press
ISBN 13 : 1420034863
Total Pages : 247 pages
Book Rating : 4.4/5 (2 download)
Download or read book American-Style Derivatives written by Jerome Detemple and published by CRC Press. This book was released on 2005-12-09 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focusing on recent developments in the field, American-Style Derivatives provides an extensive treatment of option pricing with emphasis on the valuation of American options on dividend-paying assets. This book reviews valuation principles for European contingent claims and extends the analysis to American contingent claims. It presents basic valuation principles for American options including barrier, capped, and multi-asset options. It also reviews numerical methods for option pricing and compares their relative performance. Ideal for students and researchers in quantitative finance, this material is accessible to those with a background in stochastic processes or derivative securities.
Author : Rüdiger U. Seydel
Publisher : Springer Science & Business Media
ISBN 13 : 3540279261
Total Pages : 314 pages
Book Rating : 4.5/5 (42 download)
Download or read book Tools for Computational Finance written by Rüdiger U. Seydel and published by Springer Science & Business Media. This book was released on 2006-08-07 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tools for Computational Finance offers a clear explanation of computational issues arising in financial mathematics. The new third edition is thoroughly revised and significantly extended, including an extensive new section on analytic methods, focused mainly on interpolation approach and quadratic approximation. Other new material is devoted to risk-neutrality, early-exercise curves, multidimensional Black-Scholes models, the integral representation of options and the derivation of the Black-Scholes equation. New figures, more exercises, and expanded background material make this guide a real must-to-have for everyone working in the world of financial engineering.
Author : Lars Stentoft
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (129 download)
Download or read book American Option Pricing Using GARCH Models and the Normal Inverse Gaussian Distribution written by Lars Stentoft and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we propose a feasible way to price American options in a model with time-varying volatility and conditional skewness and leptokurtosis, using GARCH processes and the Normal Inverse Gaussian distribution. We show how the risk-neutral dynamics can be obtained in this model, we interpret the effect of the risk-neutralization, and we derive approximation procedures which allow for a computationally efficient implementation of the model. When the model is estimated on financial returns data the results indicate that compared to the Gaussian case the extension is important. A study of the model properties shows that there are important option pricing differences compared to the Gaussian case as well as to the symmetric special case. A large scale empirical examination shows that our model out-performs the Gaussian case for pricing options on the three large US stocks as well as a major index. In particular, improvements are found when it comes to explaining the smile in implied standard deviations.
Author : Kumar Muthuraman
Publisher :
ISBN 13 :
Total Pages : 24 pages
Book Rating : 4.:/5 (129 download)
Download or read book A Moving Boundary Approach to American Option Pricing written by Kumar Muthuraman and published by . This book was released on 2008 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper describes a method to solve the free-boundary problem that arises in the pricing of American options. Most numerical methods for American option pricing exploit the representation of the option price as the expected pay-off under the risk-neutral measure and calculate the price for a given time to expiration and stock price. They do not solve the related free-boundary problem explicitly. The advantage of solving the free-boundary problem is that it provides the entire price function as well as the optimal exercise boundary explicitly. Our approach, which we term the Moving Boundary Approach, is based on using a boundary guess and the value associated with the guess to construct an improved boundary. It is also shown that on iteration, the sequence of boundaries converge monotonically to the optimal exercise boundary. Examples illustrating the convergence behavior as well as discussions providing insight into the method are also presented. Finally, we compare run times and speeds with other methods that solve the free-boundary problem and compute the optimal boundaries explicitly, like the front-fixing method, penalty method, method based on the integral representations and the method by Brennan and Schwartz (1977).
Author : Santtu Salmi
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (137 download)
Download or read book An Iterative Method for Pricing American Options Under Jump-Diffusion Models written by Santtu Salmi and published by . This book was released on 2012 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We propose an iterative method for pricing American options under jump-diffusion models. A finite difference discretization is performed on the partial integro-differential equation, and the American option pricing problem is formulated as a linear complementarity problem (LCP). Jump-diffusion models include an integral term, which causes the resulting system to be dense. We propose an iteration to solve the LCPs efficiently and prove its convergence. Numerical examples with Kou's and Merton's jump-diffusion models show that the resulting iteration converges rapidly.
Author : Carl Chiarella
Publisher :
ISBN 13 :
Total Pages : 19 pages
Book Rating : 4.:/5 (13 download)
Download or read book Pricing American Options Under Regime Switching Using Method of Lines written by Carl Chiarella and published by . This book was released on 2016 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper considers the American option pricing problem under regime-switching by using the method-of-lines (MOL) scheme. American option prices in each regime involve prices in all other regimes. We treat the prices from other regimes implicitly, thus guaranteeing consistency. Iterative procedures are required but very few iterative steps are needed in practice. Numerical tests demonstrate the robustness, accuracy and efficiency of the proposed numerical scheme. We compare our results with Buffington and Elliott (2002)'s analytical approximation under two regimes. Our MOL scheme provides improved results especially for out-of-the money options, possibly because they use a separation of variable approach to the PDEs which cannot hold around the early exercise region. We also compare our results with those of Khaliq and Liu (2009) and suggest that their implicit scheme can be improved.
Author : Garrett G. Smith
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (983 download)
Download or read book American Option Pricing written by Garrett G. Smith and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This study examines methods of pricing American style options, moving from the binomial model to the Black Scholes method and finishing with simulated method of option pricing. A simulated approached is based off the work established by Longstaff and Schwartz (2001) and extended by Rambharat and Brockwell (2010). Downfalls of these methods are discussed, as are ways to improve upon them. Using Monte Carlo methods and particle filtering will lead to a platform where options are priced with greater detail. Also, these simulated methods lead to faster computing time allowing for a more efficient use of resources and a theoretical framework of pricing.
Author :
Publisher :
ISBN 13 :
Total Pages : 1046 pages
Book Rating : 4.E/5 ( download)
Download or read book The Journal of Computational Finance written by and published by . This book was released on 2000 with total page 1046 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Leonid Kogan
Publisher : Forgotten Books
ISBN 13 : 9780666532459
Total Pages : 82 pages
Book Rating : 4.5/5 (324 download)
Download or read book Pricing American Options written by Leonid Kogan and published by Forgotten Books. This book was released on 2018-02-27 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from Pricing American Options: A Duality Approach The main practical contribution of this paper is a general algorithm for constructing upper and lower bounds on the true price of the option using any approximation to the option price. We show that our bounds are tight, so that if the initial approximation is close to the true price of the option, the bounds are also guaranteed to be close. In addition, we explicitly characterize the worst-case performance of the pricing bounds. The computation of the lower bound is straightforward and relies on simulating the suboptimal exercise strategy implied by the approximate option price. The upper bound is obtained by simulating a different stochastic process that is determined by choosing an appropriate supermartingale. We justify this procedure by representing the American option price as a solution of a dual minimization problem, which is the main theoretical result of this paper. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Author : Lars Stentoft
Publisher :
ISBN 13 :
Total Pages : 52 pages
Book Rating : 4.:/5 (13 download)
Download or read book American Option Pricing Using Simulation written by Lars Stentoft and published by . This book was released on 2019 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt: It contains an introduction to how simulation methods can be used to price American options and a discussion of various existing methods. An application using one of these methods, the regression based method, to the GARCH option pricing model is also provided.
Author : Christophe Chorro
Publisher : Springer
ISBN 13 : 9783662450369
Total Pages : 0 pages
Book Rating : 4.4/5 (53 download)
Download or read book A Time Series Approach to Option Pricing written by Christophe Chorro and published by Springer. This book was released on 2014-12-18 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Jingtang Ma
Publisher :
ISBN 13 :
Total Pages : 23 pages
Book Rating : 4.:/5 (13 download)
Download or read book Hybrid Laplace Transform and Finite Difference Methods for Pricing American Options Under Complex Models written by Jingtang Ma and published by . This book was released on 2017 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we propose a hybrid Laplace transform and finite difference method to price (finite-maturity) American options, which is applicable to a wide variety of asset price models including the constant elasticity of variance (CEV), hyper-exponential jump-diffusion (HEJD), Markov regime switching models, and the finite moment log stable (FMLS) models. We first apply Laplace transforms to free boundary partial differential equations (PDEs) or fractional partial differential equations (FPDEs) governing the American option prices with respect to time, and obtain second order ordinary differential equations (ODEs) or fractional differential equations (FDEs) with free boundary, which is named as the early exercise boundary in the American option pricing. Then, we develop an iterative algorithm based on finite difference methods to solve the ODEs or FDEs together with the unknown free boundary values in the Laplace space. Both the early exercise boundary and the prices of American options are recovered through inverse Laplace transforms. Numerical examples demonstrate the accuracy and efficiency of the method in CEV, HEJD, Markov regime switching models and the FMLS models.
