Efficient pricing and calibration of high-dimensional basket options

Abstract

This paper studies equity basket options–i.e. multi-dimensional derivatives whose payoffs depend on the value of a weighted sum of the underlying stocks–and develops a new and innovative approach to ensure consistency between options on individual stocks and the index comprising them. Specifically, we show how to resolve a well-known problem that when individual constituent distributions of an equity index are inferred from the single-stock option markets and combined in a multi-dimensional local/stochastic volatility model, the resulting basket option prices will not generate a skew matching that of the options on the equity index corresponding to the basket.