Grafting Information in Scenario Trees - Application to Option Prices

Abstract

The high level of sophistication in portfolio management modeling techniques often goes along with very large output sensitivity to parameter choices. As a potential solution to this problem, this paper proposes a consistent and flexible methodology to represent the distribution of future values of a portfolio through scenario trees. This methodology relies on the information contained in current option prices in order to generate the probability density function of future returns. This density function can be used, in turn, to generate scenario trees . As an illustration, a tree of scenarios based on S&P500 options is built and then used to compute arbitrage-free option prices. The approach preserves information embedded in options prices and is able to provide very accurate values for out-of-sample options. The high level of numerical accuracy of the framework is reproduced on different samples. The scenario tree approach also provides stable pricing results when confronted with the passage of time. The results derived from our model are comparable to those obtained from Rubinstein’s [1994] methodology, although both models fulfill different objectives.

Keywords: option pricing, arbitrage-free valuation, scenario trees, numerical analysis, out-of-sample testing

JEL Classification: C10, C61, G12