Importance Sampling in the Heath-Jarrow-Morton Framework

This paper develops a variance reduction technique for pricing derivatives in high-demensional multifactor models, with particular emphasis on term structure models formulated in the Heath-Jarrow-Morton framework. A premise of this work is that the largest gains in simulation efficiency come from taking advantage of the structure of both the cashflows of a security and the model in which it is priced; for this to be feasible in practice requires that the identification and use of relevant structure be automated. We exploit model and payoff structure through a combination of importance sampling and stratified sampling. The importance sampling applies a change of drift to the underlying factors; we select the drift by first solving an optimization problem. We then identify a particularly effective direction for stratified sampling (which may be thought of as an approximate numerical integration) by solving an eigenvector problem. Examples illustrate that the combination of the methods can produce some computational overhead in solving the optimization and eigenvector problems; to address this we propose and evaluate approximate solution procedures. These further enhance the applicability of the method.