| When the agents invest in the foreign capital market, studying the pricing of cross-currency Derivatives is of theoretical significance and practical value in financial mathe-matic, because of the indetermination in exshange rate and assets price.In this paper.The valuation of Foreign Equity Options in different situations is studied.The first, the process of asset price and the exchange rate are assumed to be lognormal distribution in a complete and continuous market model. Using the theory of stochastic calculus,we establish the multidimensional Black-Scholes models of Foreign Equity Options. The reciprocal stochastic differential equation and the general pricing formulas of different kinds familiar Foreign Equity Options are given.The second, considering that the randomness of interest rate influences the asset price, this paper deduces a few computational formulae of these cross-currency Options under two stochastic models of interest rate, making use of risk-neutral valuation principal and martingent methods of European options. The hedging stategy is given.The third, For the assets price and exchange rate may change discontinuously, and statistic analyse has show obvious " thick tail " distribution of the the assets price, so supposing the the assets price is Merton-jump-diffusion process , we make further study in the follow hypothesis :l)When exchange rate is also jump-diffusion process with different jumping scope,using no arbitrary method and Feynman-Kac formula.,we shown the stochastic differential equation which the options must be satisfied and the general pricing expressions.2)When the options has random life,by means of the similar stochastic analysis, the general pricing formula is obtained.3)When the assets price and exchange rate have stochastic volatility, by martingent method, the close-form solution to the valuation of options has been derived.Fanally, two kinds innovative Foreign Equity Options have been given in this paper, and the valuation is alse studied.
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