Download or read book Efficient Numerical Pricing of American Call Options Using Symmetry Arguments written by Lars Stentoft and published by . This book was released on 2019 with total page 66 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper demonstrates that it is possible to improve significantly on the estimated call prices obtained with the regression and simulation based Least-Squares Monte-Carlo method of Longstaff & Schwartz (2001) by using put-call symmetry. Results show that the symmetric method performs much better on average than the regular pricing method for a large sample of options with characteristics of relevance in real life applications, is the best method for most of the options, never performs poorly and, as a result, is extremely efficient compared to the optimal but unfeasible method that picks the method with the smallest Root Mean Squared Error (RMSE). A simple classification method is proposed that, by optimally selecting among estimates from the symmetric method with a reasonably small order used in the polynomial approximation, achieves a relative efficiency of more than 98%. The relative importance of using the symmetric method increases with option maturity and with asset volatility. Using the symmetric method to price, for example, real options, many of which are call options with long maturities on volatile assets, for example energy, could therefore improve the estimates significantly by decreasing their Bias and RMSE by orders of magnitude.
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"
Download or read book American Option Pricing Under Stochastic Volatility written by Suchandan Guha and published by . This book was released on 2008 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: ABSTRACT: We developed two new numerical techniques to price American options when the underlying follows a bivariate process. The first technique exploits the semi-martingale representation of an American option price together with a coarse approximation of its early exercise surface that is based on an efficient implementation of the least-squares Monte Carlo method. The second technique exploits recent results in the efficient pricing of American options under constant volatility. Extensive numerical evaluations show these methods yield very accurate prices in a computationally efficient manner with the latter significantly faster than the former. However, the flexibility of the first method allows for its extension to a much larger class of optimal stopping problems than addressed in this paper.
Download or read book Mathematical Modeling And Methods Of Option Pricing written by Lishang Jiang and published by World Scientific Publishing Company. This book was released on 2005-07-18 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the unique perspective of partial differential equations (PDE), this self-contained book presents a systematic, advanced introduction to 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. In particular, the qualitative and quantitative analysis of American option pricing is treated based on free boundary problems, and the implied volatility as an inverse problem is solved in the optimal control framework of parabolic equations.
Download or read book Efficient Numerical Methods for Pricing American Options Under L vy Models written by Sebastian Quecke and published by . This book was released on 2007 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Download or read book Computational Methods for Option Pricing written by Yves Achdou and published by SIAM. This book was released on 2005-01-01 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors review some important aspects of finance modeling involving partial differential equations and focus on numerical algorithms for the fast and accurate pricing of financial derivatives and for the calibration of parameters. This book explores the best numerical algorithms and discusses them in depth, from their mathematical analysis up to their implementation in C++ with efficient numerical libraries.
Download or read book Efficient Numerical Methods for Pricing American Options Under Stochastic Volatility written by Samuli Ikonen and published by . This book was released on 2005 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Nonlinear Option Pricing written by Julien Guyon and published by CRC Press. This book was released on 2013-12-19 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: New Tools to Solve Your Option Pricing ProblemsFor nonlinear PDEs encountered in quantitative finance, advanced probabilistic methods are needed to address dimensionality issues. Written by two leaders in quantitative research-including Risk magazine's 2013 Quant of the Year-Nonlinear Option Pricing compares various numerical methods for solving hi
Download or read book A Note on Relative Efficiency of Some Numerical Methods for Pricing of American Options Under Levy Processes written by Sergei Levendorskii and published by . This book was released on 2004 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt: We analyze properties of prices of American options under Levy processes, and the related difficulties for design of accurate and efficient numerical methods for pricing of American options. The case of Levy processes with insignificant diffusion component and jump part of infinite activity but finite variation (the case most relevant to practice according to the empirical study in Carr et. al., Journ. of Business (2002)) appears to be the most difficult. Several numerical methods suggested for this case are discussed and compared. It is shown that approximations by diffusions with embedded jumps may be too inaccurate unless time to expiry is large, but two methods: the fitting by a diffusion with embedded exponentially distributed jumps and a new finite difference scheme suggested in the paper can be used as good complements, which ensure accurate and fast calculation of the option prices both close to expiry and far from it. We demonstrate that if the time to expiry is 2 months or more, and the relative error 1-2% is admissible then the fitting by a diffusion with embedded exponentially distributed jumps and the calculation of prices using the semi-explicit pricing procedure in Levendorskii, IJTAF (2004), is the best choice.
Download or read book The Valuation of American Barrier Options Using the Decomposition Technique written by Marti G. Subrahmanyam and published by . This book was released on 2008 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we propose an alternative approach for pricing and hedging non-standard American options. In principle, the proposed approach applies to any kind of American-style contract for which the payoff function has a Markovian representation in the state space. Specifically, we obtain an analytic solution for the value and hedge parameters of barrier options, an important example of path-dependent options. The solution includes standard American options as a special case. The analytic formula also allows us to identify and exploit two key properties of the optimal exercise boundary - homogeneity in price parameters and time-invariance - for American options. In addition, some new put-call ``symmetryquot; relations are also derived. These properties suggest a new, efficient and integrated approach to pricing and hedging a variety of standard and non-standard American options. From an implementation perspective, this approach avoids the current practice of repetitive computation of option prices and hedge ratios. Our implementation of the analytic formula for barrier options indicates that the proposed approach is both efficient and accurate in computing option values and option hedge parameters. In some cases, our method is substantially faster than existing numerical methods with equal accuracy. In particular, the method overcomes the difficulty that existing numerical methods have in dealing with prices close to the barrier, the case where the barrier matters most.
Download or read book An Efficient Numerical Method for Pricing Long maturity American Put Options written by Ali Boudhina and published by . This book was released on 2013 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Generalised Geske Johnson Interpolation of Option Prices written by San-Lin Chung and published by . This book was released on 2006 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper describes four separate option types as special cases of Bermudans with general inter - exercise and time to final maturity. This produces a surface with European, finite American, infinite Bermudan and infinite American options as special cases. This allows Geske-Johnson 1984) two-point pricing to be extended to consider time-to-maturity as well as time - between - exercise opportunities. Due to their position on this map, infinite Bermudans are christened Arctic options and their pricing solution is presented. Numerical comparisons to benchmark methods are made for call prices under GBM although the results here hold for other processes and for both puts and calls when symmetry arguments are invoked.
Download or read book The Valuation of American Barrier Options Using The Decomposition Technique written by Bin Gao and published by . This book was released on 2001 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we propose an alternative approach for pricing and hedging American barrier options. Specifically, we obtain an analytic representation for the value and hedge parameters of barrier options, using the decomposition technique of separating the European option value from the early exercise premium. This allows us to identify some new put-call quot;symmetryquot; relations and the homogeneity in price parameters of the optimal exercise boundary. These properties can be utilized to increase the computational efficiency of our method in pricing and hedging American options. Our implementation of the obtained solution indicates that the proposed approach is both efficient and accurate in computing option values and option hedge parameters. Our numerical results also demonstrate that the approach dominates the existing lattice methods in both accuracy and efficiency. In particular, the method is free of the difficulty that existing numerical methods have in dealing with spot prices in the proximity of the barrier, the case where the barrier options are most problematic.
Download or read book Numerical Methods for American Option Pricing with Nonlinear Volatility written by Wen Wang and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation is organized as follows: Chapter 1 is an introduction to option pricing theory; Chapter 2 focuses on theoretical model of uncertain volatility; Chapter 3 introduces the numerical methods; Chapter 4 shows the experiment results; Chapter 5 summarizes the work and points out some future research directions.
Download or read book Option Pricing written by Robert A. Jarrow and published by McGraw-Hill/Irwin. This book was released on 1983 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Numerical Methods in Finance and Economics written by Paolo Brandimarte and published by John Wiley & Sons. This book was released on 2013-06-06 with total page 501 pages. Available in PDF, EPUB and Kindle. Book excerpt: A state-of-the-art introduction to the powerful mathematical and statistical tools used in the field of finance The use of mathematical models and numerical techniques is a practice employed by a growing number of applied mathematicians working on applications in finance. Reflecting this development, Numerical Methods in Finance and Economics: A MATLAB?-Based Introduction, Second Edition bridges the gap between financial theory and computational practice while showing readers how to utilize MATLAB?--the powerful numerical computing environment--for financial applications. The author provides an essential foundation in finance and numerical analysis in addition to background material for students from both engineering and economics perspectives. A wide range of topics is covered, including standard numerical analysis methods, Monte Carlo methods to simulate systems affected by significant uncertainty, and optimization methods to find an optimal set of decisions. Among this book's most outstanding features is the integration of MATLAB?, which helps students and practitioners solve relevant problems in finance, such as portfolio management and derivatives pricing. This tutorial is useful in connecting theory with practice in the application of classical numerical methods and advanced methods, while illustrating underlying algorithmic concepts in concrete terms. Newly featured in the Second Edition: * In-depth treatment of Monte Carlo methods with due attention paid to variance reduction strategies * New appendix on AMPL in order to better illustrate the optimization models in Chapters 11 and 12 * New chapter on binomial and trinomial lattices * Additional treatment of partial differential equations with two space dimensions * Expanded treatment within the chapter on financial theory to provide a more thorough background for engineers not familiar with finance * New coverage of advanced optimization methods and applications later in the text Numerical Methods in Finance and Economics: A MATLAB?-Based Introduction, Second Edition presents basic treatments and more specialized literature, and it also uses algebraic languages, such as AMPL, to connect the pencil-and-paper statement of an optimization model with its solution by a software library. Offering computational practice in both financial engineering and economics fields, this book equips practitioners with the necessary techniques to measure and manage risk.
