The Study Of Foreign Exchange Option Pricing Issue

In1973, Black and Scholes, Black-Scholes option pricing model is put forward. TheBlack-Scholes when applied to currency options pricing model is known as-G-K model.Famous Black-Scholes option pricing formula in the financial derivatives research areaoccupies very important position, however, Black-Scholes option formula defects inpractical applications, mainly stock return volatility is assumed constant. And real datashow that the distribution of stock returns to present two marked characteristics-peak andfat tail, is not in conformity with the characteristic of the standard normal distribution. Sopeople began to study is more suitable for the actual market share price behavior model,based on this, the following work has been done in this paper.First of all, for the classic model of currency options-G-K model, two methods usedto prove the conclusion: stochastic differential equation method and insurance actuarialmethod. For stochastic differential equation method: take the first currency options tosatisfy partial differential equation, the partial differential equations in the period ofvalidity for solve the problem, to transform, then apply normally Black-Scholes optionpricing model can prove the results. For insurance actuarial method: using options to takerisks in the period of validity of the cost of the security is asking the option priceprinciple, based on binary tree model, combining with the characteristics of currencyoptions, according to the principle of no arbitrage and the risk neutral, deduces the binarytree model of currency options.Second, the analysis of the binary tree model of currency options and G-K model,the relation between using the method of risk neutral principle, central limit theorem andthe related properties of the binomial model and binary tree, in selecting the appropriateincrease factor and decrease in factor and higher probability, available binary tree modelapproximation classical currency options pricing model, and prove out this connection.Finally, on the basis of previous studies on G-K model made some improvements,normal jump diffusion model is established and applied to currency options pricing. Inthe foreign exchange model assumptions and normal jump diffusion model, under theassumption of using the theories of general equilibrium market probability measure is deduced normal jump diffusion model of foreign exchange option pricing model. In thismodel is given under the formula of futures and options pricing model, and proves theconclusion.