Importance sampling for stochastic simulations
Management Science
Neuro-Dynamic Programming
Pricing American Options: A Duality Approach
Operations Research
Regression methods for pricing complex American-style options
IEEE Transactions on Neural Networks
Function-approximation-based perfect control variates for pricing American options
WSC '05 Proceedings of the 37th conference on Winter simulation
A study of variance reduction techniques for American option pricing
WSC '05 Proceedings of the 37th conference on Winter simulation
Estimating the probability of a rare event over a finite time horizon
Proceedings of the 39th conference on Winter simulation: 40 years! The best is yet to come
A New Learning Algorithm for Optimal Stopping
Discrete Event Dynamic Systems
Approximate zero-variance simulation
Proceedings of the 40th Conference on Winter Simulation
Zero-Variance Importance Sampling Estimators for Markov Process Expectations
Mathematics of Operations Research
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Monte Carlo simulation techniques that use function approximations have been successfully applied to approximately price multi-dimensional American options. However, for many pricing problems the time required to get accurate estimates can still be prohibitive, and this motivates the development of variance reduction techniques. In this paper, we describe a zero-variance importance sampling measure for American options. We then discuss how function approximation may be used to approximately learn this measure; we test this idea in simple examples. We also note that the zero-variance measure is fundamentally connected to a duality result for American options. While our methodology is geared towards developing an estimate of an accurate lower bound for the option price, we observe that importance sampling also reduces variance in estimating the upper bound that follows from the duality.