Martingale Property of Exponential Semimartingales: A Note on Explicit Conditions and Applications to Financial Models

In numerous applications positive martingales are crucial, for example when defining an equivalent change of measure. In the class of exponentials of semimartingales positive local martingales can be easily identified. However, the true martingale property is more subtle. Based on general conditions in Kallsen and Shiryaev (2002a), we derive explicit sufficient conditions for the true martingale property for a wide class of exponentials of semimartingales. Suitably for applications, the conditions are expressed in terms of the semimartingale triplet. We present two applications to mathematical finance. First, we apply the results to stochastic volatility asset price models driven by semimartingales. Second, we provide a proof of the martingale property of the Libor rates in the Levy Libor model, as well as in a semimartingale driven Libor model.     «

In numerous applications positive martingales are crucial, for example when defining an equivalent change of measure. In the class of exponentials of semimartingales positive local martingales can be easily identified. However, the true martingale property is more subtle. Based on general conditions in Kallsen and Shiryaev (2002a), we derive explicit sufficient conditions for the true martingale property for a wide class of exponentials of semimartingales. Suitably for applications, the conditio...     »