Research On Fuzzy Option Pricing

The theory of uncertainty shows that in addition to random things,fuzzy events may occur in the evolution of natural things.Random events have randomness,which is an objective uncertainty,while fuzzy events have fuzziness,which is a subjective uncertainty.Credibility theory is a theory developed for fuzzy events.It is found that there are also a lot of fuzziness in the financial market,such as the introduction of national policies,the merger of enterprises,the handling of disasters and other factors that affect the pricing of products in financial market.The introduction of fuzziness into financial market creates fuzzy finance.In view of the importance of fuzzy option pricing to actual financial market,with the aid of credibility theory,on the basis of the existing fuzzy stock model,we study the general situation of option pricing,and as an expansion,construct a new fuzzy stock model and give the option pricing.In addition,considering the fuzziness of interest rates,this paper introduces fuzzy interest rate model and fuzzy term structure,reaches the option pricing formula under fuzzy interest rate,and deduces the differential equation that the option price satisfies under the conditions of dividend payment and transaction cost.The main contents are as follows:(1)The generalized stock model driven by Liu process is studied,and the pricing formulas of European and American options are derived.(2)Establish a new stock model driven by fractional Liu process.According to the definition of expected value,the pricing formulas of European,American,Asian and power options are derived,and the corresponding numerical examples are given.(3)Study fuzzy interest rate,establish the interest rate model driven by Liu process,and obtain the corresponding term structure equation and pricing formula of bonds prices.(4)Under the promise of fuzzy interest rate,construct the option pricing model and get the price formula of European call option.Furthermore,the results are extend the stock model driven by fractional Liu process.(5)Obtain the term structure equation of European options for fuzzy stock model with dividends and transaction costs.