A Universal Pairwise Local Correlation Model

Abstract

In this paper we develop a local correlation model which uses a universal function g(t,m_i,m_j) to describe the local correlation between any asset-asset pair of a basket of underlyings. The arguments m_i,m_j are spot moneynesses.The universal function is calibrated to fit the implied volatilities of an equity index like DAX or EUROSTOXX50. The advantage of this approach is that we do not need to simulate the complete index when pricing options on a usually small subset of this index. The approach does also not suffer from the so-called chewing gum effect of correlation models where the local correlation depends on just the index value. The main part of our work is to show how to calibrate the universal function for each time step such that the resulting correlation matrices are positive definite almost anytime and that the function is sufficiently smooth to allow for stable evaluation.