Pricing Basket Options with Optimum Wavelet Correlation Measures

Abstract

This chapter describes a new procedure for designing optimum correlation measures for financial time series. The technique attempts to overcome some of the limitations in existing methods by looking at correlations among wavelet features extracted at different time scales from the underlying time series. New correlation coefficients are further optimised with help of artificial neural networks and genetic algorithms using a nonparametric adaptive wavelet thresholding scheme. The approach is applied to the problem of pricing basket options for which the pricing formula depends on accurate measurements of correlations between portfolio constituents. When compared with standard linear approaches (i.e., RiskMetrics™), an optimised predictive wavelet correlation measure offers potentially large reductions (over 50% in some cases) in static delta-hedging errors.