Accelerated Simulation for Coherent Risk Measure

Importance sampling is always used to modify the probabilities for rare event occurrences that govern the outcomes of the simulation in a way that allows for low probability events to occur more frequently. In this paper, importance sampling is applied to accelerate the simulation for coherent risk measure based on generalized rare scenarios. Firstly, we show how to combine importance sampling with ranking and selection method provided by Lesnevski, Nalson and Staum to accelerate simulation coherent risk measure directly. Secondly, recursive Robbins-Monro type algorithm is introduced to estimate the parameters of optimal sampling distributions. Finally, computational efficiency of simulated confidence intervals for coherent risk measure is discussed under three simulation settings: Asian call option, Asian options on partial average, down-and-in barrier call option.