Research On European Option Pricing Under Multifractional Stochastic Interest Rate Model

The rapid development of financial markets has led to the increasing number of financial derivatives.As a financial derivative,options are widely concerned with their leverage and hedging characteristics.On the research of option pricing,researchers use respectively Brownian motion and fractional Brownian motion model to study option pricing,but empirical studies show that both classical Brownian motion model and fractional Brownian motion model cannot accurately describe the self-similarity and long-term dependence characteristics of financial assets,while multifractional Brownian motion model can better describe the peak and tail characteristics of financial markets.Therefore,it is necessary to study the asset pricing under the multifractional Brownian motion model.In this paper,based on the financial stochastic analysis and option pricing theory,uses the multifractional stochastic interest rate model to describe the price change of financial assets.There are two parts in this paper.The first part is the proof of reasoning of the option pricing formula.Firstly,The stochastic equations are verifed by used constructing a portfolio and applying a risk-free hedging principle and stochastic differential equation theory.Then,the partial differential equations are solved by the heat conduction equation,and it is concluded that the European option pricing formula with the transaction cost and random interest rate under the mutifractional Brownian motion model.In the second part,using the 50 ETF option is used for simulation analysis.Firstly,the basic characteristics of the data are obtained by descriptive statistical analysis of the obtained data,and the values of the parameters to be estimated are obtained.Then,the classic B-S model and the extended model are used to simulate the price of the asset and comparing with the real price change path.Finally,the price of the simulated underlying asset is brought to the corresponding option pricing formula,and the price of the option is calculated and compared with the true value of the option.Compared with the classic B-S model,the option pricing under the multifractional stochastic interest rate model is closer to the true value of the option.Therefore,the model of multifractional stochastic is effective and feasible for option pricing.