The Inverse Problem of Foreign Exchange Option Pricing

Abstract

When investors apply foreign exchange options to avoid foreign exchange risk, the key issue is how to use a reasonable mathematical model to determine the price of foreign exchange options. At present, volatility is mostly determined by using subjective estimations and sample calculations. Therefore, different sources of volatility result in large differences between calculated price and the actual price of the exchange options, which will affect the strategy selection and the actual return of investors. Meanwhile, in the actual foreign exchange market, the normal distribution-based return rate cannot express the fat tail situation of volatility. This paper clarifies the inverse problem based on the fat tail of return rates of foreign exchange in option pricing. The inverse problem plays a pivotal role in determining the form of implied volatility and fluctuations in the value scope. First, this paper summarizes the present state of research on the inverse problems of foreign exchange option pricing. Second, this paper explains the basic theory of foreign exchange options, and deduce 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 puts forward a foreign exchange option pricing model based on the t-distribution and the inverse problem which is more appropriate to the actual foreign exchange market. Last the paper exemplifies the foreign exchange option pricing inverse problem based on fat tail of exchange rate return by using the numerical differential algorithm, which solves implied volatility.