The mean value of a fuzzy number
Fuzzy Sets and Systems - Fuzzy Numbers
On weighted possibilistic mean and variance of fuzzy numbers
Fuzzy Sets and Systems - Theme: Basic concepts
Pricing European options based on the fuzzy pattern of Black-Scholes formula
Computers and Operations Research
European option pricing under fuzzy environments
International Journal of Intelligent Systems
Methods and Applications of Interval Analysis (SIAM Studies in Applied and Numerical Mathematics) (Siam Studies in Applied Mathematics, 2.)
Option valuation model with adaptive fuzzy numbers
Computers & Mathematics with Applications
On theoretical pricing of options with fuzzy estimators
Journal of Computational and Applied Mathematics
A new application of fuzzy set theory to the Black-Scholes option pricing model
Expert Systems with Applications: An International Journal
Mathematical and Computer Modelling: An International Journal
Fuzzy coefficient volatility (FCV) models with applications
Mathematical and Computer Modelling: An International Journal
Modeling Chinese stock returns with stable distribution
Mathematical and Computer Modelling: An International Journal
Hi-index | 0.98 |
Owing to the fluctuations in the financial markets from time to time, some input variables, in particular the interest rate, spot exchange rate and volatility, in the Garman-Kohlhagen model [M.B. Garman, S.W. Kohlhagen, Foreign currency option values, Journal of International Money and Finance 2 (1983) 231-237] cannot be expected in a precise sense. Therefore, the fuzzy set theory introduced by Zadeh [L.A. Zadeh, Fuzzy sets, Information and Control 8 (1965) 338-353] can provide a useful tool to deal with this kind of impreciseness. In this paper, three different versions of the G-K model, the put-call parity relationship and the calculation formulas of the Greek letters according to these three different G-K models are then proposed based on fuzzy set theory. Under the considerations of fuzzy foreign and domestic interest rates, fuzzy spot exchange rate and fuzzy volatility, the European currency option prices and the Greek letters turn into fuzzy numbers or closed intervals. This means that the investors can pick any European currency option price and Greek letters with an acceptable belief degree or belief degree weighting parameter 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.