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Primal-Dual Simulation Algorithm for Pricing Multidimensional American Options

Banc of America Securities LLC, 9 West 57th Street, New York, New York 10019
Graduate School of Business, Columbia University, 3022 Broadway, New York, New York 10027-6902
leif.andersen{at}bofasecurities.com
mnb2{at}columbia.edu

This paper describes a practical algorithm based on Monte Carlo simulation for the pricing of multidimensional American (i.e., continuously exercisable) and Bermudan (i.e., discretely exercisable) options. The method generates both lower and upper bounds for the Bermudan option price and hence gives valid confidence intervals for the true value. Lower bounds can be generated using any number of primal algorithms. Upper bounds are generated using a new Monte Carlo algorithm based on the duality representation of the Bermudan value function suggested independently in Haugh and Kogan (2004) and Rogers (2002). Our proposed algorithm can handle virtually any type of process dynamics, factor structure, and payout specification. Computational results for a variety of multifactor equity and interest-rate options demonstrate the simplicity and efficiency of the proposed algorithm. In particular, we use the proposed method to examine and verify the tightness of frequently used exercise rules in Bermudan swaption markets.

Key Words: American options; Bermudan options; Bermudan swaptions; Monte Carlo simulation; Libor market model; option pricing; multiple state variables; real options
History: Received: April 18, 2003;

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