The Pricing Formula For Coupon-bonds Option Based On Hull-white Model

Option pricing has been a one hot issue in finance and computation economics.Recently, to known European options and American options, many domestic andoverseas scholars have priced options based on various asset classes. This subjectstudied on the pricing formula for Coupon-Bonds Option mainly from three stochasticprocesses: Fractional Brownian Motion, one martingale process approximate toFractional Brownian Motion and Mixed Fractional Brownian Motion.The first and second chapter includes exordium and basic knowledge. Theexordium introduces the origin of option, the history of the option pricing theory andthe development of interest-rate options pricing. Subsequently, the background and thesignificance of the selected topic are described, as well as the current research statusinland and abroad. The related theories for research are introduced at last.In third chapter, short-term interest rate is assumed satisfying the Hull-Whitemodel that is driven by Fractional Brownian Motion. According to no arbitrageprinciple and fractional Ito formula, the pricing formula of zero-coupon bond isobtained. And the pricing formula for coupon-bonds option with delay in delivery isobtained by using the methods of PDEs based on the difference between maturity anddate of delay in delivery.In chapter four, to deal with the non-martingale property of Fractional BrownianMotion, fBm is considered in Liouville form t Coupon-Bonds option pricing formula is obtained under Hull-White model by usingthe method of approximation process of assets price which is driven by fractionalBrownian motion.In fifth chapter, the mathematical model for the financial market is assumed inMixed Fractional Brownian motion setting, and the nature of noise is similar tosemimartingales. For t0, the Mixed Fractional Brownian motion is aWhen H12,1, the market, which is driven by M H t, is compete and no arbitrage.In this chapter, we obtained the pricing formula for coupon-bonds option with delay indelivery.In chapter six, main results in this dissertation is summarized and issues that needfurther improvements are pointed out.