Pricing Geometric Asian Options Under Fuzzy Stochastic Environment

Abstract

Due to the uncertainty in reality consists of randomness and fuzziness, we employ stochastic analysis and fuzzy set theory to explore the pricing of geometric Asian options. In the fuzzy stochastic world, the price of the underlying asset is assumed to follow a fuzzy stochastic process of which the classic pricing model is a special case. We derive the analytic fuzzy prices of geometric Asian options and their crisp values based on possibilistic mean. Numerical analysis shows that the degree of the fuzziness of the option prices is a increasing function in the degree of the fuzziness of the underlying price. Moreover, from the perspective of the possibilistic means of option prices, the investors are aversive to fuzziness and they ask compensation for fuzziness.