The Pricing Of Foreign Equity Options Under Multi-Jump-Diffusion Models

Foreign equity options are options whose terminal payofs, measured in domesticcurrency, depend not only on the price fluctuations of a certain foreign stock, but alsoon the future behavior of the exchange rate. When one invests in foreign stocks, he willface both the uncertainty of the foreign stock price and the uncertainty of exchange rate.It is often necessary for investors to hedge the risk of exchange rate and foreign stockprice using foreign equity options. Thus, pricing these options has become an interestingtopic. The aim of this paper is to derive the pricing formulas for foreign equity optionswith various forms of terminal payofs.In chapter2, we constructed the model under the domestic risk neutral probabilitymeasure Q, as follows: suppose the risk-free rate rd(t) and the foreign risk-free rate rf(t)follow the multidimensional Vasicek models, foreign stock price S(t) and exchange rate C(t) follow multidimensional geometry Browian motion. We then obtain the forms ofdrift terms of S(t) and C(t) by martingale method. With the It lemma and someanalytical techniques, we obtain the expressions for rd(t), rf(t), S(t) and C(t), which laythe foundation for the pricing of options.In chapter3, using Gaussian distribution properties and isometry property of the It Integral, we derive the pricing formulas for foreign equity call option written in foreigncurrency, a foreign equity call option written in domestic currency, a quanto call optionand an equity-linked foreign exchange call option. Furthermore, we obtained the put-callparity relationship, and the pricing formula of put option.Chapter4, considers the case where the assets and the exchange rate can have jumps.Using the measure transformation, martingale method and properties of It Integral,we derive the pricing formulas for the four foreign equity options described above. Inaddition, we obtain the pricing formula for the foreign equity put option by the put-callparity relationship.