Foreign Currency Options Portfolio Risk Measurement Based On Extreme Value Theory

Under the influence of the international financial environment, financial derivative products develop. Because financial supervision relaxes, Risk the investors face growing gradually. Foreign currency options are a kind of financial derivative produets, having a function of avoiding risk. And it also contains certain risk. So it is very important in foreign currency management. In our country, with a series of measures in foreign currency system reform, the fluctuation of the exchange rate to RMB expands gradually. So we should pay more attention to risk measurement of foreign currency options. When measuring risk of financial products, usually we use the VaR method, in the case of normal market; this method could estimate accurately financial products'risk according to the feature of financial products'return. But when the probability of happening extreme events is higher, accuracy of estimating financial products'risk with the VaR method would sharp declined.On the basis of summarizing method to foreign currency options at home and abroad, this paper applies the extreme theory in measuring risk of foreign currency options. And it compares simulative result and VaR of foreign currency options basis on normal market. This paper is divided into three parts:the first part:it empirical analyses statistical characteristics of benchmark exchange to Euro and Yen. It tests stability and normality with Eviews, the result finds that yield series are stable time series, but non-normal distribution. Therefore, using traditional VaR method will decline accuracy of measuring risk. The second part:it builds a model to yield series of foreign currency with Matlab and different extreme value models. On the one hand, testing tail of yield series of foreign currency with QQ figure, we find that it has heavy-tailed feature. In other words, the probability of happening extreme events is higher. On the other hand, it builds a model to yield series of foreign currency with BMM model and POT model. The third part:using FMQMC method simulates yield series of foreign currency that obey the extreme model and normal distribution, and we measure risk of foreign currency options portfolio combined with Delta-Gamma-Theta model. The basis of selecting portfolio is securities portfolio theory, in other words, we make risk minimization under certain expected rate of return. Though comparing the result of measuring foreign currency options riek under different models, and concludes are that VaR under POT model is biggest; VaR under BMM model is second; VaR under normal distribution is smallest. Therefore, in the case of existing extreme event, using traditional VaR method will underestimate risk of foreign currency options.This paper has two innovation points. On the one hand, even though many scholars have studies heavy-tail of foreign currency yield series, mainly focus on foreign exchange rate of return under t distribution, Laplace distribution or jump-diffusion process, not applying extreme value theory in the foreign currency rate of return. This paper studies risk of foreign currency options with the extreme value theory. On the other hand, because the random that Monte Carlo method simulate is fake random, having gathered feature, slow convergence speed and the defects of the large amount of calculation. So this paper uses FMQMC method to simulate data obeying the extreme value model. This paper's mainly defects lie in: when we use POT model and BMM model, parameters estimation method is observed through the intuitive, so exist certain visual error. Because of the complexity of the option pricing this paper uses BSGK model, and obtain expression of DGT model's three parameters through this model. There are certain differences between assumptions of the model and tail feature of foreign currency yield series. I hope to make the further perfection to defects in the study.