The Pricing Of Collar Options Based On Uncertain Price

With the accelerated expansion of world financial markets and the embedded devel-opment of economic globalization,forward contracts,options,futures,swaps and other financial derivatives come into being.Investors often take advantage of financial deriva-tives which have the characteristics of leverage and virtuality to speculate,arbitrage and transfer risk.Among many financial derivatives,options are an integral part of investment strategies such as hedging by investors.Therefore,the options begin to be concerned by domestic and foreign scholars for a long period.Option pricing has become one of the core issues in the field of Financial Mathematics.The Black-Scholes option pricing formula has been widely recognized since it was introduced in 1973.The model assumes that the underlying asset price follows the ge-ometric Brownian motion.However,a large number of empirical studies show that the prices of underlying asset exhibit mean regression characteristics and spike fat tailed dis-tribution.The generalized O-U process and the Geometric Fractional Brownian motion with self similarity and long-term dependence can better describe the changing charac-teristics of the underlying asset prices.Therefore,it is more significant to discuss the option pricing problem under the assumption of the above two models.Collar options and options with uncertain strike price are two kinds of low risk options in new options.We combine two options,namely,collar options with uncertain strike price.These options can further reduce the risk of options and ensure relative income.They will become a powerful tool to deal with the shock Market.In this paper,we study the pricing problem of collar options with uncertain strike price under different conditions by using the method of quasi-martingale and measure transformation.The main contents are as follows:In introduction,we introduce the development of options and pricing theory,as well as the research background,research significance,the main research content of this article.In the second chapter,we assume that the underlying asset obeys the generalized O-U process,the strike price follows the Geometric Fractional Brownian Motion.We get the pricing formulas of collar options with uncertain strike price under the time-varying parameters,and then we carry out the numerical and sensitivity analysis for relevant parameters.In the third chapter,we assume that the underlying asset and the strike price all follow the Geometric Fractional Brownian Motion.Firstly,the underlying asset and the strike price are affected by independent market factors.Secondly,the underlying asset and the strike price are affected by relevant market factors.Under the above two models we get the pricing formulas of collar options with uncertain strike price under the time-varying parameters respectively.Finally,the two models are generalized to the case with continuous dividend to carry out the numerical and sensitivity analysis for relevant parameters.In the fourth chapter,we summarize the main research results and the research characteristics of this paper,and then put forward the problems that need to be solved.