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Monte Carlo methods for the valuation of multiple-exercise options. (English) Zbl 1169.91372
Summary: We discuss Monte Carlo methods for valuing options with multiple-exercise features in discrete time. By extending the recently developed duality ideas for American option pricing, we show how to obtain estimates on the prices of such options using Monte Carlo techniques. We prove convergence of our approach and estimate the error. The methods are applied to options in the energy and interest rate derivative markets.

MSC:
91G60 Numerical methods (including Monte Carlo methods)
60G42 Martingales with discrete parameter
65C05 Monte Carlo methods
91G20 Derivative securities (option pricing, hedging, etc.)
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[1] L.Andersen, and M.Broadie(2001 ): A Primal-Dual Simulation Algorithm for Pricing Multi-Dimensional American Options . Working paper, Columbia University.
[2] Barraquand J., J. Financial Quant. Anal. 30 pp 383– (1995)
[3] Brigo D., Interest Rate Models - Theory and Practice (2001) · Zbl 1038.91040
[4] DOI: 10.1016/S0165-1889(97)00029-8 · Zbl 0901.90009
[5] M.Broadie, and P.Glasserman(1997 ): A Stochastic Mesh Method for Pricing High-Dimensional American Options . Preprint. · Zbl 0901.90009
[6] DOI: 10.1007/s007800200071 · Zbl 1039.91020
[7] Haugh M. B., Oper. Res 52 pp 258– (2001)
[8] Longstaff F. A., J. Finance 47 pp 1259– (1992)
[9] DOI: 10.1093/rfs/14.1.113 · Zbl 1386.91144
[10] Rogers L. C. G., Math. Finance 12 pp 271– (2002)
[11] Shiryaev A. N., Probability (1984) · Zbl 0536.60001
[12] Tilley J. A., Trans. Soc. Actuar. 45 pp 83– (1993)
[13] DOI: 10.1109/9.793723 · Zbl 0958.60042
[14] DOI: 10.1109/72.935083
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