A New Class of Local Correlation Models

Abstract

Allowing correlation to be local, i.e., state-dependent, in multi-asset models allows better hedging by incorporating correlation moves in the delta. When options on a basket, be it a stock index, a cross FX rate, or an interest rate spread, are liquidly traded, one may calibrate a local correlation to these option prices. In this article we introduce a new family of local correlation models from which one can pick a model that not only calibrates to the basket smile but also has extra desirable properties, like fitting a view on correlation skew, mimicking historical correlation, or matching prices of exotic options. The family is built using the particle method and the procedure is easily adapted to calibrate path-dependent volatility models, path-dependent correlation models, and to include stochastic rates, stochastic dividend yield, and stochastic volatility.