Research On Option Pricing Model Under Uncertainty And Its Application

In the real financial market, there are always other uncertain phenomena,such as fuzzy phenomenon, random phenomenon. Along with empirical studyincreasing investigator discovered that this kind of uncertainty a?ects policy-maker's behavior choice and the asset price change. Researcher pay more andmore attention to the problems on the option pricing under in uncertain environ-ments, Therefore, the dissertation shows that options can be valued successfullyin uncertain environments, some option pricing models are established, the corre-sponding algorithm is designed to solve these models. The contents are describedas follows:We discuss the existing option pricing model, and carry out a detailed anal-ysis and comparison. Then point out theirs advantages, disadvantages and im-provements.The fuzzy volatility pricing option models are proposed, in which the volatil-ity is depicted as a continuous and discrete fuzzy variable. Then we discuss themethods how to derive the expected value of fuzzy option price. In addition,fuzzy simulation techniques are designed to estimate the value of option. Finally,a numerical example is given to demonstrate the idea in the models.By considering the investor's subjective factors in process to infer Americanput option price, the fuzzy American option pricing model of discrete time andcontinues-time are established, respectively. in which the price of stocks is takenas fuzzy variables. Moreover, the expected value of option price is derived by themaking-decision attitude.A random fuzzy jump-di?usion option pricing model is proposed, where thevolatility and the jumps intensity are depicted as fuzzy variables, respectively.As a sequence, the European option price turns into the fuzzy variable. Fuzzysimulation technique is designed to estimate the membership degree and theexpected value of the option. The rough figures of the expected value of optioncan be obtained. Fuzzy L process is proposed by the credibility theory with accuracy theoret-ically proof. An option valuation model using fuzzy L process is constructed. Wedemonstrate how fuzzy L process can be successfully applied to the risk neutraloption pricing model with applying fuzzy calculus to finance.The paper presents the fuzzy random option pricing models for Europeanoption, in which the evolution of stocks price are taken as fuzzy random process.Moreover, in order to make-decision better for the investor, the expected valueof option price can be derived by the formula. We apply fuzzy random optionpricing models to warrant pricing with the empirical analysis by the Chinesesecurities historical data, and explode the input variable economical meaning.We compare the proposing model with traditional Black-Scholes model. Keywords: Uncertainty, Fuzzy theory, Option pricing model, Empirical analysis...