Download or read book Valuing American Asian Options with Least Squares Monte Carlo and Low Discrepancy Sequences written by Andries Jacobus Van Niekerk and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: There exists no closed form approximation for arithmetically calculated Asian options, but research has shown that closed form approximations are possible for Geometrically calculated Asian options. The aim of this dissertation is to effectively price American Asian options with the least squares Monte Carlo approach (Longstaff & Schwartz, 2001), applying Low discrepancy sequences and variance reduction techniques. We evaluate how these techniques affect the pricing of American options and American Asian options in terms of accuracy, computational efficiency, and computational time used to implement these techniques. We consider the effect of, Laguerre-, weighted Laguerre- , Hermite-, and Monomial-basis functions on the Longstaff and Schwartz (2001) model. We briefly investigate GPU optimization of the Longstaff and Schwartz algorithm within Matlab. We also graph the associated implied and Local volatility surfaces of the American Asian options to assist in the practical applicability of these options.
Download or read book Valuing Bermuda Asian Options by Least Squares Monte Carlo Simulation written by 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 Comparisons of Alternative Quasi Monte Carlo Sequences for American Option Pricing written by Jennifer X.F. Jiang and published by . This book was released on 2004 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quasi-Monte Carlo sequences have been shown to provide accurate option price approximations for a variety of options. In this paper, we apply quasi-Monte Carlo sequences in a duality approach to value American options. We compare the results using different low discrepancy sequences and estimate error bounds and computational effort. The results demonstrate the value of sequences using expansions of irrationals.
Download or read book On Improving the Least Squares Monte Carlo Option Valuation Method written by Nelson Areal and published by . This book was released on 2018 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper studies various possible approaches to improving the least squares Monte Carlo option valuation method. We test different regression algorithms and suggest a variation to estimating the option continuation value, which can reduce the execution time of the algorithm by one third. We test the choice of varying polynomial families with different number of basis functions. We compare several variance reduction techniques, and find that using low discrepancy sequences can improve the accuracy up to four times. We also extend our analysis to compound and mutually exclusive options. For the latter, we propose an improved algorithm which is faster and more accurate.
Download or read book Least Squares Monte Carlo and Quasi Monte Carlo Method in Pricing American Put Options Using Matlab written by Phuc Phan and published by . This book was released on 2016 with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this report, we evaluate the use of the Least Squares Monte Carlo (LSM) method, which was proposed by Longstaff and Schwartz in 2001. The holder of an American option has the right to exercise the option anytime, which makes the option much more difficult to price compared to a European style option. LSM is a simple and powerful method to price American style options and utilizes the use of least squares to estimate the conditional expected payoff to the option holder from continuation value. I provide a simple version of the LSM algorithm using second degree polynomials as basis functions with working code in Matlab to price American put option. I illustrate how the model is affected when input parameter such as risk free interest rate, volatility, underlying stock price, time to maturity are perturbed. After that, I construct the quasi Monte Carlo version of the Least Square algorithm by using Halton sequence and compare the performance of both quasi Monte Carlo and Monte Carlo algorithm.
Download or read book Assessing the Least Squares Monte Carlo Approach to American Option Valuation written by Lars Stentoft and published by . This book was released on 2001 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Convergence of the Least Squares Monte Carlo Approach to American Option Valuation written by Lars Stentoft and published by . This book was released on 2002 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book American Asian Option Pricing Based on Monte Carlo Simulation Method written by Shiguang Han and published by . This book was released on 2012 with total page 65 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Monte Carlo Method for Pricing American Options written by Diego Garcia and published by . This book was released on 1999 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Pricing American Options by Canonical Least Squares Monte Carlo written by Qiang Liu and published by . This book was released on 2008 with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt: Options pricing and hedging under canonical valuation have recently been demonstrated to be quite effective, but unfortunately are only applicable to European options. In this paper, a variation of canonical valuation called canonical least-squares Monte Carlo is proposed to price American options, which proceeds in three stages. First, given a set of historical gross returns (or price ratios) of the underlying for a chosen time interval, a discrete risk-neutral distribution is obtained via the canonical approach. Second, from this canonical distribution independent random samples of gross returns are taken to simulate future price paths for the underlying. Third, to those paths the least-squares Monte Carlo method is then applied to compute a price for an American option. Numerical results obtained from using simulated gross returns under geometric Brownian motion (GBM) show that this new approach yields reasonably accurate prices for American put options and can be utilized as an alternative to pricing American options, whether the underlying follows GBM or not.
Download or read book A Workout in Computational Finance written by Andreas Binder and published by John Wiley & Sons. This book was released on 2013-08-13 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive introduction to various numerical methods used in computational finance today Quantitative skills are a prerequisite for anyone working in finance or beginning a career in the field, as well as risk managers. A thorough grounding in numerical methods is necessary, as is the ability to assess their quality, advantages, and limitations. This book offers a thorough introduction to each method, revealing the numerical traps that practitioners frequently fall into. Each method is referenced with practical, real-world examples in the areas of valuation, risk analysis, and calibration of specific financial instruments and models. It features a strong emphasis on robust schemes for the numerical treatment of problems within computational finance. Methods covered include PDE/PIDE using finite differences or finite elements, fast and stable solvers for sparse grid systems, stabilization and regularization techniques for inverse problems resulting from the calibration of financial models to market data, Monte Carlo and Quasi Monte Carlo techniques for simulating high dimensional systems, and local and global optimization tools to solve the minimization problem.
Download or read book Numerical Probability written by Gilles Pagès and published by Springer. This book was released on 2018-07-31 with total page 591 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides a self-contained introduction to numerical methods in probability with a focus on applications to finance. Topics covered include the Monte Carlo simulation (including simulation of random variables, variance reduction, quasi-Monte Carlo simulation, and more recent developments such as the multilevel paradigm), stochastic optimization and approximation, discretization schemes of stochastic differential equations, as well as optimal quantization methods. The author further presents detailed applications to numerical aspects of pricing and hedging of financial derivatives, risk measures (such as value-at-risk and conditional value-at-risk), implicitation of parameters, and calibration. Aimed at graduate students and advanced undergraduate students, this book contains useful examples and over 150 exercises, making it suitable for self-study.
Download or read book On the Robustness of Least Squares Monte Carlo LSM for Pricing American Derivatives written by Manuel Moreno and published by . This book was released on 2007 with total page 41 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper analyses the robustness of Least - Squares Monte Carlo, a technique proposed by Longstaff and Schwartz (2001) for pricing American options. This method is based on least - squares regressions in which the explanatory variables are certain polynomial functions. We analyze the impact of different basis functions on option prices. Numerical results for American put options show that this approach is quite robust to the choice of basis functions. For more complex derivatives, this choice can slightly affect option prices.
Download or read book Pricing American style Moving average Options with Least square Monte Carlo Simulation Approaches written by 王志鴻 and published by . This book was released on 2003 with total page 76 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Quasi Monte Carlo Approaches to Option Pricing written by John R. Birge and published by . This book was released on 1995 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On the Dangers of a Simplistic American Option Simulation Valuation Method written by Nelson Areal and published by . This book was released on 2018 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Chen and Shen (2003) argue that it is possible to improve the Least Squares Monte Carlo Method (LSMC) of Longstaff and Schwartz (2001) to value American options by removing the least squares regression module. This would make not only faster but also more accurate. We demonstrate, using a large sample of 2500 put options that the proposed algorithm - the Perfect Foresight Method (PFM) - is, as argued by the authors, faster than the LSMC algorithm but, contrary to what they state, it is not more accurate than the LSMC. In fact, the PFM algorithm incorrectly prices American options, resulting in an upward biased value of the option. We therefore, do not recommend the use of the PFM.
Download or read book On the Robustness of Least squares Monte Carlo LSM for Pricing American Derivatives written by Manuel Moreno (Economista) and published by . This book was released on 2001 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
