Pricing perpetual American-type strangle option for merton's jump diffusion process

Abstract

A stock price Xt evolves according to jump diffusion process with certain parameters. An asset manager who holds a strangle option on that stock, wants to maximize his/her expected payoff over the infinite time horizon. We derive an optimal exercise rule for asset manager when the underlying stock is dividend paying and non-dividend paying. We conclude that optimal stopping strategy changes according to stock’s dividend rate. We also illustrate the solution on numerical examples.