American-style Asian Options Under Jump-diffusion Processes

In this book we derive the analytical solutions to the American-style Asian Options under jump-diffusion processes. The similar problem was studied by Hansen and Jorgensen (2000), but they considered the diffusion case. First of all we transform the problem into one-state variable problem (the dual problem). To this new problem, we find its general analytical solution by using theories from Hansen and Jorgensen (2000), Merton (1976) and H. Pham. Also we derive the analytical solutions to the particular cases, when the average is geometric and arithmetic. In the arithmetic average case, the one-state variable is not a geometric Brownian motion, so we approximate it to a geometric Brownian motion by using the Wilkisson aproximation. At the end of this book we have some numerical results comparing the earlier exercise boundaries in diffusion and jump-diffusion cases.