Greeks Analysis of Currency Option under Fuzzy Environment

Owing to the fluctuations in the financial markets from time to time, some input variables such as the interest rate, spot exchange rate and volatility in the Garman-Kohlhagen model can not be expected in a precise sense. Therefore, it is nature to start from the fuzzy environments of currency options markets. In this paper, we introduce fuzzy techniques and obtain the fuzzy versions of the Garman-Kohlhagen model. The calculation formulas of the Greek letters according to the fuzzy G-K models are obtained based on fuzzy set theory. By assuming the foreign and domestic interest rates, spot exchange rate and volatility as fuzzy numbers, the European currency option prices and the Greek letters turn into fuzzy numbers. Then the financial investors can pick any European currency option price and Greek letters with an acceptable belief degree for his later use. The empirical results indicate that the Greeks calculated under fuzzy environment can be considered as a useful tool for managing option risk for an option writer.