A Variance Reduction Technique Based on Integral Representations

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A Variance Reduction Technique Based on Integral Representations

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David Heath
Eckhard Platen () (School of Finance and Economics, University of Technology, Sydney)

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Eckhard Platen

Abstract

Standard Monte Carlo methods can often be significantly improved with the addition of appropriate variance reduction techniques. In this paper a new and powerful variance reduction technique is presented. The method is based directly on the Ito calculus and is used to find unbiased variance reduced estimators for the expectation of functionals of Ito diffusion processes. The approach considered has wide applicability, for instance, it can be used as a means of approximating solutions of parabolic partial differential equations or applied to valuation problems that arise in mathematical finance. We illustrate how the method can be applied by considering the pricing of European style derivative securities for a class of stochastic volatility models, including the Heston model.

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Paper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 75.

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Date of creation: 01 Mar 2002
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Handle: RePEc:uts:rpaper:75

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Find related papers by JEL classification:
G12 - Financial Economics - - General Financial Markets - - - Asset Pricing

References listed on IDEAS
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Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 14(1), pages 113-47.
Boyle, Phelim & Broadie, Mark & Glasserman, Paul, 1997. "Monte Carlo methods for security pricing," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1267-1321, June. [Downloadable!] (restricted)
N. Hofmann & E. Platen & M. Schweizer, 1992. "Option Pricing under Incompleteness and Stochastic Volatility," Discussion Paper Serie B 209, University of Bonn, Germany.
Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 6(2), pages 327-43. [Downloadable!] (restricted)

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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

David Heath & Eckhard Platen, 2004. "Local Volatility Function Models under a Benchmark Approach," Research Paper Series 124, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
Other versions:
- David Heath & Eckhard Platen, 2006. "Local volatility function models under a benchmark approach," Quantitative Finance, Taylor and Francis Journals, vol. 6(3), pages 197-206, June. [Downloadable!] (restricted)
Gao, Jiti, 2002. "Modeling long-range dependent Gaussian processes with application in continuous-time financial models," MPRA Paper 11973, University Library of Munich, Germany, revised 18 Sep 2003. [Downloadable!]

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