Conditional simulation for moving average processes with discrete or continuous values

Abstract

A conditional simulation technique has previously been presented for variance reduction when estimating tail probabilities, particularly extreme ones, for a wide class of moving-average processes. Here, we generalize the technique from continuous to discrete random variables. Two distinct approaches to this generalization are presented and compared. We describe some of the empirical properties of the preferred method in simple examples, and present some more general examples including autoregressive moving-average processes in one and two dimensions. We show that the technique performs well for processes with a wide range of structures, provided the tail probability to be estimated is not too large. We discuss briefly the application of this technique in investigating volatility in financial models of, for example, asset prices.