A Variance Reduction Technique Based on Integral Representations
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.
|Date of creation:||01 Mar 2002|
|Publication status:||Published as: Heath, D. and Platen, E., 2002, "A Variance Reduction Technique Based on Integral Representations", Quantitative Finance, 2(5), 362-369.|
|Contact details of provider:|| Postal: PO Box 123, Broadway, NSW 2007, Australia|
Phone: +61 2 9514 7777
Fax: +61 2 9514 7711
Web page: http://www.qfrc.uts.edu.au/
More information through EDIRC
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.:
- Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-147.
- 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.
- Norbert Hofmann & Eckhard Platen & Martin Schweizer, 1992.
"Option Pricing Under Incompleteness and Stochastic Volatility,"
Wiley Blackwell, vol. 2(3), pages 153-187.
- 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, Society for Financial Studies, vol. 6(2), pages 327-343.
- Corwin Joy & Phelim P. Boyle & Ken Seng Tan, 1996. "Quasi-Monte Carlo Methods in Numerical Finance," Management Science, INFORMS, vol. 42(6), pages 926-938, June.
- Dwight Grant & Gautam Vora & David Weeks, 1997. "Path-Dependent Options: Extending the Monte Carlo Simulation Approach," Management Science, INFORMS, vol. 43(11), pages 1589-1602, November.
- Broadie, Mark & Glasserman, Paul, 1997. "Pricing American-style securities using simulation," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1323-1352, June.
- Platen, Eckhard, 1995. "On weak implicit and predictor-corrector methods," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 38(1), pages 69-76.
- Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA. Full references (including those not matched with items on IDEAS)