Research On The Inverse Problem Of Foreign Exchange Option Pricing

With the collapse of the Bretton Woods system, the Western countries generally began to introduce floating exchange rate system. In floating exchange rate system ,the exchange rate is determined by the foreign exchange market supply and demand entirely, not by government intervention. A foreign exchange options became into being the emerging financial derivatives to avoid foreign exchange risk. Investors in the foreign exchange options market buy or sell foreign exchange options with a means to reduce their foreign exchange risk in the transaction. The key issue that investors apply foreign exchange options to avoid foreign exchange risk is how to use a reasonable mathematical model to determine the price of foreign exchange options, but in the calculation process, due to different volatility, calculate and determine the result of the price and the actual foreign exchange options price have large differences. Meanwhile, in the actual foreign exchange market, the normal rate of return can not express the fat tail, so this paper studies the inverse problem based on the fat tail of return exchange rates of foreign exchange option pricing to determine the form of implied volatility and fluctuations in the value scope ,it is very important.Firstly, this paper summarizes and evaluates the research status of the foreign exchange option pricing inverse problems at home and abroad;Secondlly,this paper summarizes the basic theory of foreign exchange options, and deduced a positive foreign exchange option pricing problem,that is G-K foreign exchange option pricing.At the same time,it proposes the inverse problem of foreign exchange option pricing, then, improve the inverse problem of foreign exchange options pricing, through the t-distribution based on the foreign exchange option pricing model, it uses model of the fat tail of return based on foreign exchange options pricing, proposed inverse problem of foreign exchange options pricing,through the numerical differentiation method and select data from commercial banks in the euro against the dollar and the pound against the U.S.,that is dollar spot exchange rate S , the exercise priceK , maturity , its risk-free interest rater , the foreign risk-free interest rateTr f,the actual volatility of the actual data, based on substitution t-distribution theory of implied volatility value, use MATLAB to get the 3D surface map of implied volatility. The results show that in the foreign exchange options market, the implied volatility fluctuates within a certain range, rather than a straight line, and the implied volatility have different forms in different currencies, provides a reference for selecting the appropriate volatility at future foreign exchange options pricing to reduce the risk of operating funds.