A Large Market Model with Stochastic Volatility and Application to Pricing Credit Derivatives

Abstract

We investigate a Large Market Model with Stochastic Volatility given by Heston dynamics. We introduce two correlated market drivers: one corresponding to the assets and one corresponding to the volatilities. By passing to the limit with the number of assets, we derive a Stochastic Partial Differential Equation (SPDE) governing the behaviour of the two dimensional limit density. We define the loss process as a functional of this density. We discretize the SPDE in order to price selected complex credit derivatives: Single Tranche Collateralized Debt Obligations (CDOs) and Forward Start CDOs. We study the impact of varying model parameters on the loss process and the pricing.