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Analysing the bias in the primal-dual upper bound method for early exercisable derivatives: bounds, estimation and removal

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  • Mark S. Joshi

Abstract

We analyse the primal-dual upper bound method for Bermudan options and prove that its bias is inversely proportional to the number of paths in sub-simulations for a large class of cases. We develop a methodology for estimating and reducing the bias. We present numerical results showing that the new technique is indeed effective.

Suggested Citation

  • Mark S. Joshi, 2016. "Analysing the bias in the primal-dual upper bound method for early exercisable derivatives: bounds, estimation and removal," Quantitative Finance, Taylor & Francis Journals, vol. 16(4), pages 519-533, April.
    • Handle: RePEc:taf:quantf:v:16:y:2016:i:4:p:519-533
    DOI: 10.1080/14697688.2015.1086490
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    References listed on IDEAS

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    1. Carriere, Jacques F., 1996. "Valuation of the early-exercise price for options using simulations and nonparametric regression," Insurance: Mathematics and Economics, Elsevier, vol. 19(1), pages 19-30, December.
    2. Nan Chen & Paul Glasserman, 2007. "Additive and multiplicative duals for American option pricing," Finance and Stochastics, Springer, vol. 11(2), pages 153-179, April.
    3. Mark S. Joshi, 2007. "A Simple Derivation of and Improvements to Jamshidian's and Rogers' Upper Bound Methods for Bermudan Options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(3), pages 197-205.
    4. Denis Belomestny & Mark Joshi & John Schoenmakers, 2015. "Addendum to: Multilevel dual approach for pricing American style derivatives," Finance and Stochastics, Springer, vol. 19(3), pages 681-684, July.
    5. Mark Broadie & Menghui Cao, 2008. "Improved lower and upper bound algorithms for pricing American options by simulation," Quantitative Finance, Taylor & Francis Journals, vol. 8(8), pages 845-861.
    6. Denis Belomestny & John Schoenmakers & Fabian Dickmann, 2013. "Multilevel dual approach for pricing American style derivatives," Finance and Stochastics, Springer, vol. 17(4), pages 717-742, October.
    7. 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.
    8. Leif Andersen & Mark Broadie, 2004. "Primal-Dual Simulation Algorithm for Pricing Multidimensional American Options," Management Science, INFORMS, vol. 50(9), pages 1222-1234, September.
    9. 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.
    10. Beveridge, Christopher & Joshi, Mark & Tang, Robert, 2013. "Practical policy iteration: Generic methods for obtaining rapid and tight bounds for Bermudan exotic derivatives using Monte Carlo simulation," Journal of Economic Dynamics and Control, Elsevier, vol. 37(7), pages 1342-1361.
    11. Kin Hung (Felix) Kan & R. Mark Reesor, 2012. "Bias Reduction for Pricing American Options by Least-Squares Monte Carlo," Applied Mathematical Finance, Taylor & Francis Journals, vol. 19(3), pages 195-217, July.
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    14. Joshi, Mark & Tang, Robert, 2014. "Effective sub-simulation-free upper bounds for the Monte Carlo pricing of callable derivatives and various improvements to existing methodologies," Journal of Economic Dynamics and Control, Elsevier, vol. 40(C), pages 25-45.
    15. L. C. G. Rogers, 2002. "Monte Carlo valuation of American options," Mathematical Finance, Wiley Blackwell, vol. 12(3), pages 271-286, July.
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