Extremum Options Pricing In A Jump-diffusion Model

Option is a contract that gives the holder the right, but not obligation to buy or sell the underlying asset by a certain date for a certain price. As an important tool of portfolio and risk management, option is more and more widely used. The pricing of option has also become an important issue in academic research. Since Black and Scholes proposed the classic B-S model in 1973, the theory of option pricing has been rapidly developed. However, it has been clear that the B-S model fails to reflect the real market with discontinuous and non-stationary information. One way to capture the facts is to assume that the risky asset return dynamics follows a jump-diffusion model.Merton(1976) firstly incorporated the compound Poisson process into the jump-diffusion model, and got more realistic results under such a model.Extremum option is a multi-asset option, whose payoff depends on the highest or lowest price of the underlying assets. The pricing work was firstly proposed by Stulz(1982) and Johnson(1987), whose studies were both under B-S model. This paper considers the pricing of both European and American extremum op-tion under a jump-diffusion model, includes the following main contents:Chapter 1 introduces the research background and significance of the topic, and describes some necessary preliminaries.Chapter 2 considers the pricing of European extremum option when the underly-ing assets follow a jump-diffusion process. We discuss two-asset extremum option at first, derive the valuation formulas for two-asset maximum call(put) option and minimum call(put) option, then extend the results to the case of n-asset. Numerical results are provided at the end.Chapter 3 considers the pricing of American extremum option under the jump- diffusion model, derives the valuation formula for two-asset American maximum put option, then provides the numerical results.Chapter 4 summarizes the contents of this paper and introduces some issue to be further studied.