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Abstract
In this article, we explain how the importance sampling technique can be generalized from simulating expectations to computing the initial value of backward stochastic differential equations (SDEs) with Lipschitz continuous driver. By means of a measure transformation we introduce a variance reduced version of the forward approximation scheme by Bender and Denk [Citation4] for simulating backward SDEs. A fully implementable algorithm using the least-squares Monte Carlo approach is developed and its convergence is proved. The success of the generalized importance sampling is illustrated by numerical examples in the context of Asian option pricing under different interest rates for borrowing and lending.
Thilo Moseler was supported by the DFG (Deutsche Forschungsgemeinschaft) as member of the research unit 518 “Price, Liquidity and Credit Risks: Measurement and Distribution.” He is also grateful to Robert Denk for attracting his attention to this problem and for many fruitful discussions.
Christian Bender gratefully acknowledges partial support by the DFG priority programme 1324 “Mathematische Methoden zur Extraktion quantifizierbarer Information aus komplexen Systemen.”