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American Option Pricing with Importance Sampling and Shifted Regressions

Author

Listed:
  • Francois-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

This paper proposes a new method for pricing American options that uses importance sampling to reduce estimator bias and variance in simulation-and-regression based methods. Our suggested method uses regressions under the importance measure directly, instead of under the nominal measure as is the standard, to determine the optimal early exercise strategy. Our numerical results show that this method successfully reduces the bias plaguing the standard importance sampling method across a wide range of moneyness and maturities, with negligible change to estimator variance. When a low number of paths is used, our method always improves on the standard method and reduces average root mean squared error of estimated option prices by 22.5 % .

Suggested Citation

  • Francois-Michel Boire & R. Mark Reesor & Lars Stentoft, 2021. "American Option Pricing with Importance Sampling and Shifted Regressions," JRFM, MDPI, vol. 14(8), pages 1-21, July.
    • Handle: RePEc:gam:jjrfmx:v:14:y:2021:i:8:p:340-:d:599073
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    References listed on IDEAS

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    1. Moreni, Nicola, 2004. "A variance reduction technique for American option pricing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 338(1), pages 292-295.
    2. 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.
    3. 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.
    4. 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.
    5. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    6. 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.
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    Cited by:

    1. Yan, Dong & Lin, Sha & Hu, Zhihao & Yang, Ben-Zhang, 2022. "Pricing American options with stochastic volatility and small nonlinear price impact: A PDE approach," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).

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