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Bermudan options by simulation

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  • L. C. G. Rogers

Abstract

The aim of this study is to devise numerical methods for dealing with very high-dimensional Bermudan-style derivatives. For such problems, we quickly see that we can at best hope for price bounds, and we can only use a simulation approach. We use the approach of Barraquand & Martineau which proposes that the reward process should be treated as if it were Markovian, and then uses this to generate a stopping rule and hence a lower bound on the price. Using the dual approach introduced by Rogers, and Haugh & Kogan, this approximate Markov process leads us to hedging strategies, and upper bounds on the price. The methodology is generic, and is illustrated on eight examples of varying levels of difficulty. Run times are largely insensitive to dimension.

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  • L. C. G. Rogers, 2015. "Bermudan options by simulation," Papers 1508.06117, arXiv.org, revised Jan 2016.
  • Handle: RePEc:arx:papers:1508.06117
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    References listed on IDEAS

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    1. Leif Andersen & Mark Broadie, 2004. "Primal-Dual Simulation Algorithm for Pricing Multidimensional American Options," Management Science, INFORMS, vol. 50(9), pages 1222-1234, September.
    2. 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.
    3. Barraquand, Jérôme & Martineau, Didier, 1995. "Numerical Valuation of High Dimensional Multivariate American Securities," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 30(03), pages 383-405, September.
    4. Jin, Xing & Li, Xun & Tan, Hwee Huat & Wu, Zhenyu, 2013. "A computationally efficient state-space partitioning approach to pricing high-dimensional American options via dimension reduction," European Journal of Operational Research, Elsevier, vol. 231(2), pages 362-370.
    5. Svetlana Boyarchenko & Sergei LevendorskiĬ, 2013. "American Options in the Heston Model with Stochastic Interest Rate and Its Generalizations," Applied Mathematical Finance, Taylor & Francis Journals, vol. 20(1), pages 26-49, March.
    6. Jèôme Barraquand, 1995. "Numerical Valuation of High Dimensional Multivariate European Securities," Management Science, INFORMS, vol. 41(12), pages 1882-1891, December.
    7. L. C. G. Rogers, 2002. "Monte Carlo valuation of American options," Mathematical Finance, Wiley Blackwell, vol. 12(3), pages 271-286.
    8. Farshid Jamshidian, 2004. "Numeraire-invariant option pricing and american, bermudan, trigger stream rollover (v1.6)," Finance 0407015, EconWPA.
    9. Medvedev, Alexey & Scaillet, Olivier, 2010. "Pricing American options under stochastic volatility and stochastic interest rates," Journal of Financial Economics, Elsevier, vol. 98(1), pages 145-159, October.
    10. 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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