Pricing And Hedging In Affine Models With Possibility Of Default
The authors propose a general class of models for the simultaneous treatment of equity, corporate bonds, government bonds and derivatives. The noise is generated by a general affine Markov process. The framework allows for stochastic volatility, jumps, the possibility of default and correlations between different assets. They extend the notion of a discounted moment generation function of the log stock price to the case where the underlying can default and show how to calculate it in terms of a coupled system of generalized Riccati equations. This yields an efficient method to compute prices of power payoffs and Fourier transforms.