UC San Diego

The Russian option is a lookback option which pays the maximum-to-date of the underlying, subject to some discounting factor. In this thesis we examine the properties of the value function for the Russian option problem in a jump-diffusion model, generalizing the results of Peskir (2004). In particular, we use the theory of viscosity solutions to show that the value function is smooth inside the continuation region. Furthermore, we show that optimal stopping boundary can be characterized as the unique solution to a free boundary problem under the same assumptions given in Pham (1998) for the American put option