This talk provides a definition and complete characterization of regular affine processes, a class of Markov processes that has arisen from a large and growing range of useful applications in finance, although until now without succinct mathematical foundations. The key ``affine'' property is roughly that the characteristic function of the transition distribution of such a process is exponential-affine with respect to the initial state. This includes continuous-state branching processes with immigration and processes of the Ornstein-Uhlenbeck type in particular. Some common financial applications of the properties of a regular affine process include: the term structure of interest rates, the pricing of options and credit risk. Prominent examples are the Vasicek and Cox-Ingersoll-Ross short rate models and Heston's stochastic volatility model.

Modelling Credit Risk In Convertible Bonds

Gerald Quinlan, Sungard Trading and Risk Systems

The correct way of including credit risk in convertible bond pricing has always been a source of confusion. One approach is to use a model that considers the full 'value of the firm', including information about the issuer's distance to default. These models require information about the issuer's capital structure, however, and must make simplifying assumptions to reduce the problem to a tractable form. The more commonly used approach is to add a credit spread to the risk-free yield curve. Several ad-hoc procedures have been proposed for splitting the credit spread between the bond and option parts of the convertible. These are reviewed and compared with a more consistent treatment of credit risk in the convertible security. The use of stock-dependent credit spreads is shown to be necessary for matching price profiles of real convertibles. A different approach is required for exchangeable bonds - convertibles for which the stock and bond are issued by different firms. Conclusions are drawn for the measurement and hedging of credit risk in convertible portfolios.