Minimal Partial Proxy Simulation Schemes for Generic and Robust Monte-Carlo Greeks

In this paper, we present a generic framework known as the minimal partial proxy simulation scheme. This framework allows for a stable computation of the Monte-Carlo Greeks for financial products with trigger features via finite difference approximation. The minimal partial proxy simulation scheme can be considered as a special case of the partial proxy simulation scheme (Fries and Joshi, 2008b) where measure changes (weighted Monte-Carlo) are performed to prevent pathwise discontinuities. However, our approach differs in term of how these measure changes are performed. Specifically, we select the measure changes optimally such that they minimise the variance of the Monte-Carlo weights. Our method can be applied to popular classes of trigger products including digital caplets, autocaps and target redemption notes. While the Monte-Carlo Greeks obtained using the partial proxy simulation scheme can blow up in certain cases, these Monte-Carlo Greeks remain stable under the minimal partial proxy simulation scheme. The standard errors of vegas are also significantly lower under the minimal partial proxy simulation scheme