The Pricing Model Of Reload Option

In1973, the option pricing model is established by Black and Scholes, and thepricing formula is also given by assuming that the underlying asset price followed ageometric fractional Brownian motion. Black-Scholes formula marks the forming ofoption pricing theory framework. In recent years, some scholars believe that thestochastic differential equations driven by fractional Brownian motion to describe thechanges in asset prices is more rational.In this article, asset prices, which follow a stochastic differential equation drivenby fractional Brownian motion, are assumed, then mathematical models of financialmarkets are established in fractional Brownian motion environment by stochasticanalysis theory with the fractional Brownian motion, and the reload option pricingproblem is studied by using actuarial pricing methods. The paper is divided into fivechapters.In chapter one, the development and study of option, the development andresearch of reload option are introduced, the main content of the topics is alsointroduced.In chapter two, the definition, characteristic and stochastic integral of fractionalBrownian motion are introduced, the insurance actuary method for European optionpricing are also introduced.In chapter three, underlying asset price process follows stochastic differentialequation driven by fractional Brownian motion, the financial market mathematicalmodel is built by the stochastic analysis theory for fractional Brownian motion, Usingphysical probabilistic measure of price process and the principle of fair premium, thepricing formula of reload option in fractional Brownian motion environment isobtained.In chapter four, underlying asset price follows a fractional jump-diffusionprocess where the expected rate, the volatility rate and the risk-less rate are time function. The financial market model is built by the stochastic analysis theory forfractional Brownian motion. Using physical probabilistic measure of price processand the principle of fair premium, the pricing formula for reload option is obtained.In chapter five, the main results are summarized in this article and some issues,which need further improvement, are pointed out.