Simulation Modeling and Analysis
Simulation Modeling and Analysis
Approximating Martingales for Variance Reduction in Markov Process Simulation
Mathematics of Operations Research
Pricing American Options: A Duality Approach
Operations Research
Function-approximation-based perfect control variates for pricing American options
WSC '05 Proceedings of the 37th conference on Winter simulation
Pricing American-Style Derivatives with European Call Options
Management Science
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We develop a class of control variates for the American option pricing problem that are constructed through the use of MARS -- multivariate adaptive regression splines. The splines approximate the option's value function at each time step, and the value function approximations are then used to construct a martingale that serves as the control variate. Significant variance reduction is possible even in high dimensions. The primary restriction is that we must be able to compute certain one-step conditional expectations.