Rene Carmona (Princeton University)

HJM: A Unified Approach to Dynamic Models for Fixed Income, Credit and Equity Markets

Abstract: The purpose of the talk is to highlight some of the key elements of the HJM approach as originally introduced in the framework of fixed income market models, to explain how the very same philosophy was implemented in the case of credit portfolio derivatives and to show how it can be extended to and used in the case of equity market models. In each case we show how the HJM approach naturally yields a consistency condition and a no-arbitrage conditions in the spirit of the original work of Heath, Jarrow and Morton. Even though the actual computations and the derivation of the drift condition in the case of equity models seems to be new, the lecture is mostly pedagogical in nature emphasizing the philosophy of the approach.