The Warrants Pricing Theory

As a financial derivatives, warrant is an effectual means which internationalizes the securities business in China. With the development of the warrant market in China, pricing for warrant becomes increasingly important. Based on option pricing theory of Black-Scholes, warrant pricing in complete market was further researched in this paper.The main work includes the following contents:(1) Derived the binomial pricing formula of double-barrier knockout option;(2) Derived the pricing formula of warrant with extendible maturity;(3) Derived and analyzed by examples the warrant pricing formula based on the stock structure in China in Geometric Fractional Brownian Motion environment.Firstly, the discrete binomial model of double-barrier knockout call in classical Black-Scholes market was discussed, and its pricing formula was deduced by method of martingale pricing technique. Furthermore, the relation between this pricing formula and the pricing formula of up-and-out call, the one between this pricing formula and the pricing formula of down-and-out call and the one between this pricing formula and the pricing formula of standard European call were clarified. We defined and priced a kind of exotic warrant by using the binomial model of double-barrier knockout option and got its fair price at t=0. Secondly, the warrant with extendible maturity based on the frame of European equity warrant pricing was defined, and its pricing formula was deduced by the use of martingale pricing technique and some related knowledge of probability theory. The model of warrants with extendible maturity was analysed, and some properties of this model were led.At last, a new European equity warrant pricing model in It(o|^) Fractional Black-Scholes market was deduced by the classial option pricing theory of Black-Scholes, meanwhile, the stock structure in China, dilution effect and especial items of warrant were also taken into account synthetically. It was proposed and proved that with the exist of uncurrent stock, the latest current stock issued would make the degressive extent of price of current stock larger, accordingly reduced the value of warrant. We took Changdian warrant as an example, and the compute result showed that the new pricing model was more effective than the traditional one.