The Pricing Model Of Options And Its Application In Uncertain Environment

A new model for options with uncertainty of both randomness and fuzziness is presented in this paper. Owing to the fluctuation of financial market from time to time, the stock price and the risk-free interest rate may occur imprecisely in the real world. Therefore, it is natural to consider the theory of fuzzy stochastic processes. So the randomness and fuzziness are evaluated by both probabilistic expectation and fuzzy expectation. Base on the traditional pricing model, a new pricing formula for option is given by using the extension principle in fuzzy sets theory. Taking account of decision-maker's subjective judgment, the rational expected price of option and the optimal exercise time for American options are derived using two models. To give an example for the application, the warrant pricing using the fuzzy model is proposed in the last chapter. The numerical analysis of an actual warrant from the real financial market shows that the fuzzy models presented in this paper should do better than the Black-Scholes model in forecasting market price.