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Based on the modification of some assumptions in the traditional Black-Scholes option pricing model, we construct a model that is closer to the real financial market in this paper. That is to say, in order to make up for the shortages of using the standard Brownian motion to describe the underlying asset price, we use fractional Brownian motion to replace the standard Brownian motion in the traditional Black-Scholes model. At the same time, we assume that the interest rate satisfies the Vasicek interest rate model under fractional Brownian motion. Under the above market model, we use the stochastic analysis method under fractional Brownian motion to obtain the pricing formulae of European simple option and complex option, which generalize the existing conclusions. It is not only can be closer to the actual financial market but also make the research more practical. In addition, since the sensitivity analysis of options refers to the sensitivity or response of options to the change of its determinants, we use numerical methods to analyze the impact of the stock initial price, the chooser date and Hurst parameter on the price of European complex chooser option, which not only verifies the rationality of the pricing formula but also has guiding value for option trading.

Pricing and Analysis of European Chooser Option Under The Vasicek Interest Rate Model