Derivative Pricing with Multivariate Stochastic Volatility : Application to Credit Risk

This paper extends to the multiasset framework the closed-form solution for options withstochastic volatility derived in Heston (1993) and Ball and Roma (1994). This extensionintroduces a risk premium in the return equation and considers Wishart dynamics for theprocess of the stochastic volatility matrix, which is the multiasset analogue of the model ofCox, Ingersoll, and Ross (1985). This approach is used to extend Merton’s model (Merton(1974)) for corporate default to a framework with stochastic liability, stochastic volatilityand several firms.