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Monte Carlo methods for pricing and hedging American options in high dimension

Monte Carlo methods for pricing and hedging American options in high dimension We numerically compare some recent Monte Carlo algorithms devoted to the pricing and hedging American options in high dimension. In particular, the comparison concerns the quantization method of Barraquand–Martineau and an algorithm based on Malliavin calculus. The (pure) Malliavin calculus algorithm improves the precision of the computation of the delta but, merely for pricing purposes, is uncompetitive with respect to other Monte Carlo methods in terms of computing time. Here, we propose to suitably combine the Malliavin calculus approach with the Barraquand–Martineau algorithm, using a variance reduction technique based on control variables. Numerical tests for pricing and hedging American options in high dimension are given in order to compare the different methodologies. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Risk and Decision Analysis iospress

Monte Carlo methods for pricing and hedging American options in high dimension

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Publisher
IOS Press
Copyright
Copyright © 2011 by IOS Press, Inc
ISSN
1569-7371
eISSN
1875-9173
DOI
10.3233/RDA-2011-0044
Publisher site
See Article on Publisher Site

Abstract

We numerically compare some recent Monte Carlo algorithms devoted to the pricing and hedging American options in high dimension. In particular, the comparison concerns the quantization method of Barraquand–Martineau and an algorithm based on Malliavin calculus. The (pure) Malliavin calculus algorithm improves the precision of the computation of the delta but, merely for pricing purposes, is uncompetitive with respect to other Monte Carlo methods in terms of computing time. Here, we propose to suitably combine the Malliavin calculus approach with the Barraquand–Martineau algorithm, using a variance reduction technique based on control variables. Numerical tests for pricing and hedging American options in high dimension are given in order to compare the different methodologies.

Journal

Risk and Decision Analysisiospress

Published: Jan 1, 2011

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