Monte Carlo payoff smoothing for pricing autocallable instruments

Abstract

In this paper we develop a Monte-Carlo method to price instruments with discontinuous payoffs and non-smooth trigger functions which allows for a stable computation of Greeks via finite differences. The method extends the idea of smoothing the payoff as in Glasserman's book on Monte-Carlo methods to the multivariate case. This is accomplished by a coordinate transform and a one-dimensional analytic treatment with respect to the locally most important coordinate and Monte-Carlo sampling with respect to other coordinates. In contrast to other approaches our method does not use importance sampling. This allows to re-use simulated paths to price other instruments or for the computation of finite difference Greeks leading to massive savings in compuational cost. Not using importance sampling leads to a certain bias which is usually very small. We give a numerical analysis of this bias and show that simple local time grid refinement is sufficient to keep the bias always within low limits. Numerical experiments show that our method gives stable finite difference greeks even for situations with payoff discontinuities close to the valuation date.