Event Details

We 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. We 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. European calls and puts as well as binaries and asset-or-nothing options can then be priced with the fast Fourier transform methods of Carr and Madan (1999) and Lee (2005). Other European payoffs can be approximated by a linear combination of power payoffs and vanilla options. We show the results to be superior to using only power payoffs or vanilla options. We also give conditions for our models to be complete if enough financial instruments are liquidly tradable and study dynamic hedging strategies. As an example we discuss a Heston-type stochastic volatility model with possibility of default and stochastic interest rates.

Speaker: Alexander Wugalter, Princeton University (ORFE)

Slides: (TBA)