Research on the valuation of derivatives for jump diffusion processes

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I studied a model of valuing derivatives which enable both an issuer and an investor to exercise their rights, respectively. I dealt with the pricing of Russian options and Game Russian options for jump diffusion processes. Game Russian option is a contract in which both of the seller and the buyer have the rights to cancel and to exercise at any time, respectively. The pricing of such an option can be formulated as an optimal stopping problem between the seller and the buyer, and is analyzed as Dynkin Game. I derived the value function of Game Russian options and their optimal boundaries with jumps. Moreover, I considered a cash management problem where the cash demand is assumed to be a Brownian motion with drift and a jump diffusion process with jumps. Moreover, I discussed the effect of jumps on the optimal policy through some numerical examples.