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Efficient Numerical Pricing of American Call Options Using Symmetry Arguments

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  • Lars Stentoft

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

Abstract

This paper demonstrates that it is possible to improve significantly on the estimated call prices obtained with the regression and simulation-based least-squares Monte Carlo method by using put-call symmetry. The results show that, for a large sample of options with characteristics of relevance in real-life applications, the symmetric method performs much better on average than the regular pricing method, is the best method for most of the options, never performs poorly and, as a result, is extremely efficient compared to the optimal, but unfeasible method that picks the method with the smallest Root Mean Squared Error (RMSE). A simple classification method is proposed that, by optimally selecting among estimates from the symmetric method with a reasonably small order used in the polynomial approximation, achieves a relative efficiency of more than 98 % . The relative importance of using the symmetric method increases with option maturity and with asset volatility. Using the symmetric method to price, for example, real options, many of which are call options with long maturities on volatile assets, for example energy, could therefore improve the estimates significantly by decreasing their bias and RMSE by orders of magnitude.

Suggested Citation

  • Lars Stentoft, 2019. "Efficient Numerical Pricing of American Call Options Using Symmetry Arguments," Journal of Risk and Financial Management, MDPI, Open Access Journal, vol. 12(2), pages 1-26, April.
  • Handle: RePEc:gam:jjrfmx:v:12:y:2019:i:2:p:59-:d:221155
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    References listed on IDEAS

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    1. 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.
    2. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.),Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    3. 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.
    4. Orlin J. Grabbe, "undated". "The Pricing of Call and Put Options on Foreign Exchange," Rodney L. White Center for Financial Research Working Papers 06-83, Wharton School Rodney L. White Center for Financial Research.
    5. Wiggins, James B., 1987. "Option values under stochastic volatility: Theory and empirical estimates," Journal of Financial Economics, Elsevier, vol. 19(2), pages 351-372, December.
    6. Orlin Grabbe, J., 1983. "The pricing of call and put options on foreign exchange," Journal of International Money and Finance, Elsevier, vol. 2(3), pages 239-253, December.
    7. Schroder, Mark, 1999. "Changes of Numeraire for Pricing Futures, Forwards, and Options," Review of Financial Studies, Society for Financial Studies, vol. 12(5), pages 1143-1163.
    8. Boyle, Phelim P. & Tse, Y. K., 1990. "An Algorithm for Computing Values of Options on the Maximum or Minimum of Several Assets," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 25(2), pages 215-227, June.
    9. Scott, Louis O., 1987. "Option Pricing when the Variance Changes Randomly: Theory, Estimation, and an Application," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(4), pages 419-438, December.
    10. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
    11. Orlin J. Grabbe, "undated". "The Pricing of Call and Put Options on Foreign Exchange," Rodney L. White Center for Financial Research Working Papers 6-83, Wharton School Rodney L. White Center for Financial Research.
    12. 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.
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    Cited by:

    1. Lars Stentoft, 2020. "Computational Finance," Journal of Risk and Financial Management, MDPI, Open Access Journal, vol. 13(7), pages 1-4, July.

    More about this item

    Keywords

    least-squares Monte Carlo; put-call symmetry; regression; simulation;

    JEL classification:

    • C - Mathematical and Quantitative Methods
    • E - Macroeconomics and Monetary Economics
    • F2 - International Economics - - International Factor Movements and International Business
    • F3 - International Economics - - International Finance
    • G - Financial Economics

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