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 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 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 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 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 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 American Put Options written by Donna Salopek and published by CRC Press. This book was released on 1997-03-15 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: An American put option gives its owner the right to sell a share of stock at a given specified price on or before a given date. This book provides a detailed comparison of recent works on the American put option from both theoretical and computational approaches.
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.
Download or read book Numerical Methods for Pricing American Put Options Under Stochastic Volatility written by Dominique Joubert and published by . This book was released on 2013 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Early exercise boundary -- Free boundary value problem -- Linear complimentary problem -- Crank-Nicolson finite difference method -- Projected Over-Relaxation method (PSOR) -- Stochastic volatility -- Heston stochastic volatility model -- Vroeë uitoefengrens -- Vrye grenswaardeprobleem -- Linêere komplimentêre probleem -- Crank-Nicolson eindige differensiemetode -- Geprojekteerde oorverslappingsmetode (PSOR) -- Stogastiese volatiliteit -- Heston stogastiese volatiliteitsmodel.
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 Fractional Calculus written by Dumitru Baleanu and published by World Scientific. This book was released on 2012 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: This title will give readers the possibility of finding very important mathematical tools for working with fractional models and solving fractional differential equations, such as a generalization of Stirling numbers in the framework of fractional calculus and a set of efficient numerical methods.
Download or read book An Improved Method for Pricing and Hedging American Options written by Tommaso Paletta and published by . This book was released on 2014 with total page 45 pages. Available in PDF, EPUB and Kindle. Book excerpt: The majority of quasi-analytic pricing methods for American options are efficient near-maturity but are prone to larger errors when time-to-maturity increases. A new methodology, called the "extension"-method, is introduced to increase the accuracy of almost any existing quasi-analytic approach in pricing long-maturity American options. It relies on an approximation of the optimal exercise price near the beginning of the contract combined with existing pricing approaches so that the maturity range for which small errors are attainable is extended. The new methodology retains the quasi-analytic nature of the methods it improves on and we derive generic quasi-analytic formulae for the price of an American put as well as for its delta parameter. Our numerical study indicates that the proposed methodology considerably improves both the pricing and the hedging performance of a number of established approaches for a wide range of maturities. Furthermore, the pricing improvements are most sizeable at longer maturities, where existing approaches do not perform well.
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 Pricing and Trading American Put Options Under Sub optimal Exercise Policies written by Wei Xing and published by . This book was released on 2012 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: No analytical expression has been found for the optimal exercise boundary of finite maturity American put options. This thesis evaluates the performance of approximating the optimal boundary with a class of analytically tractable sub-optimal exercise boundaries which admit known first passage time density functions. The performance is evaluated in two steps, first by computing and comparing the value of the put option under the sub-optimal exercise policy to existing numerical approximation methods such as the binomial price, then by examining the profit/loss of a trader that would result from hedging and trading strategies based on the suboptimal exercise policy. We discovered that the valuation results from sub-optimal boundary exercise is very close to the binomial price. A closed form expression for the delta of the American put under sub-optimal exercise is derived, and the formula is remarkably close to the true numerical delta at significantly reduced computational time.
Download or read book A Numerical Method for American Option Pricing Under CEV Model written by Jing Zhao and published by . This book was released on 2007 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book American Options in L vy Models with Stochastic Interest Rates written by Svetlana Boyarchenko and published by . This book was released on 2008 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt: A general numerical method for pricing American options in regime-switching jump-diffusion models of stock dynamics with stochastic interest rates and/or volatility is developed. Time derivative and infinitesimal generator of the process for factors that determine the dynamics of the interest rate and/or volatility are discretized. The result is a sequence of embedded perpetual options in a Markov-modulated Leacute;vy model. Options in this sequence are solved using an iteration method based on the Wiener-Hopf factorization. An explicit algorithm for the case of positive stochastic interest rates driven by a process of the Ornstein-Uhlenbeck type is derived. Efficiency of the method is illustrated with numerical examples.
Download or read book The First Passage Approach to Valuing the American Put Option written by David S. Bunch and published by . This book was released on 2008 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We express the American put price as an integral involving first-passage probabilities. This approach allows us an intuitive interpretation to Merton's result for the perpetual put. We also consider the finite-lived case, derive a differential equation for the critical-stock-price function, and develop candidate analytical solutions that satisfy conditions which occur for short and long times to maturity. We present numerical results demonstrating that these solutions for the critical-stock-price functions and numerical integration of the first-passage probability expression to compute accurate prices for American put options.
