Research On The Pricing Of Reload Option

With the development of the financial market,traditional options have become difficult to meet the needs of enterprises and investors for the earnings of the financial market.Therefore,financial institutions continue to launch new financial derivatives,and many new options are generated accordingly.As a new type of option,reload option gradually comes into people's view.Its advantage is that it allows option holders to lock in profits on the reload date,and eliminates the risk that they may receive only a lower income at maturity.In order to make the reload option pricing model more suitable for the actual market,the constant interest rate is extended to random interest rate.Assume that the stock price processes are driven by mixed fractional Brownian motion and Ornstein-Uhlenbeck(O-U)process,we discuss the risk-neutral pricing and actuarial pricing of the reload option respectively.The main research contents are as follows:First,assuming that the underlying asset price process satisfies a Stochastic Differential Equation(SDE)driven by mixed fractional Brownian motion and the risk-free interest rate r is a constant,the pricing formula of the reload option at time t is obtained by the risk-neutral pricing principle.Some of the parameters are numerically analyzed.Secondly,under the principle of risk-neutral pricing and assume that the price of the underlying asset pricing process is subject to a SDE driven by mixed fractional Brownian motion and the interest rate is subject to Vasicek model,the pricing formula of the reloaded option at time 0 is obtained by the approach of change of measure.In this model,we improve the traditional actuarial pricing formula and obtain its pricing formula at time 0 by the theory of stochastic analysis.Some parameters and the two pricing results are numerically analyzed.Finally,assuming that the underlying asset price process satisfies a SDE driven by generalized O-U process and the interest rate follows Vasicek model,the pricing formula of the reload option at time 0 is obtained by the approach of change of measure.Under this model,the actuarial pricing formula of the reload option at time 0 is calculated by the theory of stochastic analysis.Some parameters and the two pricing results are numerically analyzed.