Pricing Of Binary Option Under Fractional O-U Process

The idea of replacing Brownian motion with another Gaussian process in the usualfnancial models has been around for some time.Because the stock price has long-rangedependence,fractional Brownian motion(FBM) can be considered.As it has better behavedtails and exhibits long-term dependence while remaining Gaussian.Besides,the standardBrownian motion is one special case of the FBM,which is FBM with Hurst parameter1/2.Taking the mean reverting behavior into account,we can consider the fractional O-U process.When the expected rate of return depends on the underlying assets,we call itfractional O-U process.This article mainly discusses Binary option pricing problem under the fractional O-Uprocess which includes the following contents:The frst chapter presents the fnancial mathematics history and development,as wellas the status quo of FBM.The second chapter of this article mainly introduces prior knowledge,including thebasic knowledge about the stochastic processes martingale theory and the defnition andproperty of FBM,and introduces the corresponding stochastic integral theory.The third chapter introduces the fractional O-U process model and the European op-tion pricing model with changing exercise prices,obtain the mathematical analysis pricingformula of European options.The fourth chapter describes the defnition of the extended Vasicek model and Binaryoptions, consider the pricing issues about binary option and the option with power payofat the time of maturity, fnally,we obtain the mathematical analysis pricing formula ofBinary options when the interest rate follows the extended Vasicek model.