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Faster Comparison of Stopping Times by Nested Conditional Monte Carlo

  • Fabian Dickmann
  • Nikolaus Schweizer
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    We show that deliberately introducing a nested simulation stage can lead to significant variance reductions when comparing two stopping times by Monte Carlo. We derive the optimal number of nested simulations and prove that the algorithm is remarkably robust to misspecifications of this number. The method is applied to several problems related to Bermudan/American options. In these applications, our method allows to substantially increase the efficiency of other variance reduction techniques, namely, Quasi-Control Variates and Multilevel Monte Carlo.

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    Paper provided by in its series Papers with number 1402.0243.

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    Date of creation: Feb 2014
    Date of revision:
    Handle: RePEc:arx:papers:1402.0243
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    1. Mark Broadie & Yiping Du & Ciamac C. Moallemi, 2011. "Efficient Risk Estimation via Nested Sequential Simulation," Management Science, INFORMS, vol. 57(6), pages 1172-1194, June.
    2. Denis Belomestny & Fabian Dickmann & Tigran Nagapetyan, 2013. "Pricing American options via multi-level approximation methods," Papers 1303.1334,, revised Dec 2013.
    3. Leif Andersen & Mark Broadie, 2004. "Primal-Dual Simulation Algorithm for Pricing Multidimensional American Options," Management Science, INFORMS, vol. 50(9), pages 1222-1234, September.
    4. Michael B. Gordy & Sandeep Juneja, 2008. "Nested simulation in portfolio risk measurement," Finance and Economics Discussion Series 2008-21, Board of Governors of the Federal Reserve System (U.S.).
    5. 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 113-47.
    6. repec:esr:wpaper:rsnote2012/3/1 is not listed on IDEAS
    7. 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.
    8. Youyi Feng & Guillermo Gallego, 1995. "Optimal Starting Times for End-of-Season Sales and Optimal Stopping Times for Promotional Fares," Management Science, INFORMS, vol. 41(8), pages 1371-1391, August.
    9. Denis Belomestny, 2009. "Pricing Bermudan options using nonparametric regression: optimal rates of convergence for lower estimates," Papers 0907.5599,
    10. L. C. G. Rogers, 2002. "Monte Carlo valuation of American options," Mathematical Finance, Wiley Blackwell, vol. 12(3), pages 271-286.
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