Author : Bhojnarine Rambharat
Publisher :
ISBN 13 :
Total Pages : 43 pages
Book Rating : 4.:/5 (13 download)
Book Synopsis Sequential Monte Carlo Pricing of American-Style Options Under Stochastic Volatility Models by : Bhojnarine Rambharat
Download or read book Sequential Monte Carlo Pricing of American-Style Options Under Stochastic Volatility Models written by Bhojnarine Rambharat and published by . This book was released on 2013 with total page 43 pages. Available in PDF, EPUB and Kindle. Book excerpt: We introduce a new method to price American-style options on underlying investments governed by stochastic volatility (SV) models. The method does not require the volatility process to be observed. Instead, it exploits the fact that the optimal decision functions in the corresponding dynamic programming problem can be expressed as functions of conditional distributions of volatility, given observed data. By constructing statistics summarizing information about these conditional distributions, one can obtain high quality approximate solutions. Although the required conditional distributions are in general intractable, they can be arbitrarily precisely approximated using sequential Monte Carlo schemes. The drawback, as with many Monte Carlo schemes, is potentially heavy computational demand. We present two variants of the algorithm, one closely related to the well-known least-squares Monte Carlo algorithm of Longstaff and Schwartz (2001), and the other solving the same problem using a “brute force” gridding approach. We estimate an illustrative SV model using Markov chain Monte Carlo (MCMC) methods for three equities. We also demonstrate the use of our algorithm by estimating posterior distributions of the market price of volatility risk for each of the three equities.