Pricing Exchange Options Under A Combined Model With Jump-Risks In Two Factor Market Structure

In 1973, Black and Scholes, as the pioneers, have established the celebrated op-tion pricing formula which leads to the financial derivatives market being developed rapidly. There are a great number of financial derivatives with flexible transactions and convenient prices in the market. Financial derivatives are popular because of their good features in hedging, price developments, risk management and transfer. Option is an important financial derivative which is widely used. Evaluate these options under appropriate model, its academical value and social economic signif-icance are well-know. As the classical Black-Scholes model is established basing on the geometric Brownian motion and assumed to be constant in the market struc-ture, which fail to capture the reality, while a large number of empirical studies have proved the market share price change is not fit lognormal distribution, but shows a "leptokurtic, fat tail" phenomenon. Modifying the Black-Scholes model's as-sumption to capture the reality better has become a key topic in mathematical fi-nancial area. Until now, all of the improvements are focused on three aspects, one is to add the stochastic volatility in Black-Scholes model, the second is to add the jump-diffusion model, the third is to add random risk. However most of improved models are base on a single-factor interest rates model, many empirical studys show that two-factor term structure model can describe the real market structure better. Exchange options is a investment portfolio option which contain two-asset, it gives its holder the right to exchange a given quantity of A asset for a given quantity of B asset, so as to achieve risk-averse and hedging. The option pricing of multi-asset is cheaper and far more complex than one-asset, but an option contract in practical market is often subject to prices change of several underlying basic products, there-fore, the study of the muli-asset option pricing model has an important theoretical value and practical significance. In this paper, we propose a combined model in which the underlying stock's price follows the jump-diffusion model and the mar-ket structure includes two factors with random risks that affect both the underlying stock's volatility and the interest rate. Pricing exchange options under combined model with jump risk two-factor market structure, and the propose major work and conclusions.Chapter 1, describes the necessity and significance of research in option pricing states research situation on exchange option, and the causes for choosing this title, the research content and study framework.chapter 2, pricing exchange options under combined model with jump risks two-factor market structure, we employ the fourier inversion transform, practical differ-ential equation and Feynman-kac equation study European exchange option and contain their solutions and give some numerical examples.chapter 3, the pricing of American exchange option are considered under com-bined model with jump risks two-factor market structure. As American exchange options's holder can choose when to exercise the option, so it is very difficult to ob-tain American exchange options's closed form solution. A way to estimate the value of American exchange option base on combining a European exchange option and a Bermudan exchange option with two exercise dates.chapter 4, it sums our main conclusions and further research work are summa-rized.