Monte-Carlo Payoff-Smoothing for Pricing Autocallable Instruments

23 Pages Posted: 5 May 2015 Last revised: 9 Jun 2015

Multiple version iconThere are 2 versions of this paper

Date Written: May 5, 2015

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.

Keywords: Monte Carlo Simulation, Pricing, Greeks, Variance Reduction, Payoff-Smoothing, Importance-Sampling, Auto-Callable, Trigger Product

JEL Classification: C15, G13

Suggested Citation

Koster, Frank and Rehmet, Achim, Monte-Carlo Payoff-Smoothing for Pricing Autocallable Instruments (May 5, 2015). Available at SSRN: https://ssrn.com/abstract=2602905 or http://dx.doi.org/10.2139/ssrn.2602905

Frank Koster (Contact Author)

DGZ-DekaBank ( email )

Mainzer Landstr. 16
D-60325 Frankfurt
Germany

Achim Rehmet

DGZ-DekaBank ( email )

Mainzer Landstr. 16
D-60325 Frankfurt
Germany

Do you have negative results from your research you’d like to share?

Paper statistics

Downloads
764
Abstract Views
2,434
Rank
60,880
PlumX Metrics