EQUITY CORRELATIONS IMPLIED BY INDEX OPTIONS: ESTIMATION AND MODEL UNCERTAINTY ANALYSIS
Résumé
We propose a method for constructing an arbitrage-free multiasset pricing model which is consistent with a set of observed single- and multiasset derivative prices. The pricing model is constructed as a random mixture of N reference models, where the distribution of mixture weights is obtained by solving a well-posed convex optimization problem. Application of this method to equity and index options shows that, whereas multivariate diffusion models with constant correlation fail to match the prices of index and component options simultaneously, a jump-diffusion model with a common jump component affecting all stocks enables to do so. Furthermore, we show that even within a parametric model class, there is a wide range of correlation patterns compatible with observed prices of index options. Our method allows, as a by product, to quantify this model uncertainty with no further computational effort and propose static hedging strategies for reducing the exposure of multiasset derivatives to model uncertainty.