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Leave-One-Out Least Square Monte Carlo Algorithm for Pricing American Options

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  • Jeechul Woo
  • Chenru Liu
  • Jaehyuk Choi

Abstract

The least square Monte Carlo (LSM) algorithm proposed by Longstaff and Schwartz (2001) is widely used for pricing American options. The LSM estimator contains undesirable look-ahead bias, and the conventional technique of removing it necessitates doubling simulations. We present the leave-one-out LSM (LOOLSM) algorithm for efficiently eliminating look-ahead bias. We also show that look-ahead bias is asymptotically proportional to the regressors-to-simulation paths ratio. Our findings are demonstrated with several option examples, including the multi-asset cases that the LSM algorithm significantly overvalues. The LOOLSM method can be extended to other regression-based algorithms improving the LSM method.

Suggested Citation

  • Jeechul Woo & Chenru Liu & Jaehyuk Choi, 2018. "Leave-One-Out Least Square Monte Carlo Algorithm for Pricing American Options," Papers 1810.02071, arXiv.org, revised Sep 2020.
    • Handle: RePEc:arx:papers:1810.02071
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    References listed on IDEAS

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    1. Boyle, Phelim P., 1988. "A Lattice Framework for Option Pricing with Two State Variables," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 23(1), pages 1-12, March.
    2. Brennan, Michael J & Schwartz, Eduardo S, 1977. "The Valuation of American Put Options," Journal of Finance, American Finance Association, vol. 32(2), pages 449-462, May.
    3. Boyle, Phelim P & Evnine, Jeremy & Gibbs, Stephen, 1989. "Numerical Evaluation of Multivariate Contingent Claims," The Review of Financial Studies, Society for Financial Studies, vol. 2(2), pages 241-250.
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    Cited by:

    1. Zhiyi Shen & Chengguo Weng, 2019. "A Backward Simulation Method for Stochastic Optimal Control Problems," Papers 1901.06715, arXiv.org.

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