Option Pricing When Correlations are Stochastic: An Analytical Framework

Abstract

In this paper we develop a novel market model where asset variances-covariances evolve stochastically. In addition shocks on asset return dynamics are assumed to be linearly correlated with shocks driving the variance-covariance matrix.

Analytical tractability is preserved since the model is linear-affine and the conditional characteristic function can be determined explicitly.

Quite remarkably, the model provides prices of vanilla options consistent with the smile and skew effects observed, while making possible to detect and quantify the correlation risk in multiple asset derivatives like basket options. In particular it can reproduce the asymmetric conditional correlations effect documented in Ang and Chen (2002) for equity markets.

We exemplify analytical tractability providing explicit pricing formulas for rainbow Best-of options.

Keywords: Wishart processes, Best-of Basket option, Stochastic Correlation, FFT

JEL Classification: G12, G13