Fast Computation of Univariate Memory Autocallable Notes

Abstract

In this paper we consider the valuation of a special type of equity-linked notes, so-called Memory Autocallable Notes. In contrast to the common Autocallable Notes these notes contain a memory feature that allows the recovery of any missed coupon payment. In this context, our first result is a general mathematical formulation of the cash flows. Since the Monte Carlo simulation is an appropriate tool for the valuation of Memory Autocallable Notes, the reduction of computational time for a given accuracy is of practical interest. We show that this could be reached with either the Antithetic Sampling technique or the Importance Sampling method. This is also true for the multivariate case. Furthermore, we demonstrate how to calculate the sensitivities of Memory Autocallable Notes ("Greeks") more effectively.