A fuzzy set approach on pricing american put options on Euribor futures

Abstract

A fuzzy set approach is applied to price American put options on Euribor futures in this paper. Since volatility in any option pricing model should be the future volatility, it is imprecisely to substitute history volatility or implied volatility for future volatility. We introduce an uncertainty degree to fuzzificate the volatility parameter of the option pricing model into a triangular fuzzy number. Applying the fuzzy set theory, we calculate the risk-neutral probabilities, which are obtained as fuzzy numbers. Under fuzzy probabilities, we perform the risk-neutral valuation of the American put option in a multi-period binomial model. At last, an empirical research is studied to compare the actual price of put options on 3-month Euribor futures with the theory price of both fuzzy and precision binomial option pricing model. The empirical research results indicate that fuzzy pricing model is better than precision pricing model at the low strike prices, and the low boundary of the fuzzy price is useful to price the American put options on 3-month Euribor futures.