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Efficient Variance Reduction for American Call Options Using Symmetry Arguments

Author

Listed:
  • François-Michel Boire

    (Department of Statistical and Actuarial Sciences, University of Western Ontario, London, ON N6A 5B7, Canada)

  • R. Mark Reesor

    (Department of Mathematics, Wilfrid Laurier University, Waterloo, ON N2L 3C7, Canada)

  • Lars Stentoft

    (Department of Statistical and Actuarial Sciences, University of Western Ontario, London, ON N6A 5B7, Canada
    Department of Economics, University of Western Ontario, London, ON N6A 5C2, Canada)

Abstract

Recently it was shown that the estimated American call prices obtained with regression and simulation based methods can be significantly improved on by using put-call symmetry. This paper extends these results and demonstrates that it is also possible to significantly reduce the variance of the estimated call price by applying variance reduction techniques to corresponding symmetric put options. First, by comparing performance for pairs of call and (symmetric) put options for which the solution coincides, our results show that efficiency gains from variance reduction methods are different for calls and symmetric puts. Second, control variates should always be used and is the most efficient method. Furthermore, since control variates is more effective for puts than calls, and since symmetric pricing already offers some variance reduction, we demonstrate that drastic reductions in the standard deviation of the estimated call price is obtained by combining all three variance reduction techniques in a symmetric pricing approach. This reduces the standard deviation by a factor of over 20 for long maturity call options on highly volatile assets. Finally, we show that our findings are not particular to using in-sample pricing but also hold when using an out-of-sample pricing approach.

Suggested Citation

  • François-Michel Boire & R. Mark Reesor & Lars Stentoft, 2021. "Efficient Variance Reduction for American Call Options Using Symmetry Arguments," JRFM, MDPI, vol. 14(11), pages 1-21, October.
  • Handle: RePEc:gam:jjrfmx:v:14:y:2021:i:11:p:504-:d:660556
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    References listed on IDEAS

    as
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    3. 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.
    4. Lars Stentoft, 2004. "Assessing the Least Squares Monte-Carlo Approach to American Option Valuation," Review of Derivatives Research, Springer, vol. 7(2), pages 129-168, August.
    5. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," The Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-147.
    6. Lars Stentoft, 2004. "Convergence of the Least Squares Monte Carlo Approach to American Option Valuation," Management Science, INFORMS, vol. 50(9), pages 1193-1203, September.
    7. Barraquand, Jérôme & Martineau, Didier, 1995. "Numerical Valuation of High Dimensional Multivariate American Securities," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 30(3), pages 383-405, September.
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