Option Pricing Of Two-period Stochastic Volatility Under Rationed Shares Condition

Finance has been continuously developing and reforming since its birth.Fi-nancial derivatives gradually become an important tool for risk management.The option is just an important member of various derivatives.The pricing problem of options is also a very significant topic in the field of financial derivative assets.How to apply the optimized option pricing model and better financial derivatives to the actual investment risk management control,which is extremely significant for China’s economic market.The research in this theories has important theoretical significance and academic value.An option is a right that gives the option holder the right to buy or sell the underlying asset at a predetermined purchase price.The value of an option can be seen as two parts:the intrinsic value and the time value of the option.The total value of the option can be regarded as the sum of the two parts.The factors affecting the value of the option mainly include the following five points:the price of the underlying assetSt,the execution price K,the expiration time T,the risk-free rate of return r,and the volatility of the underlying asset priceσ.Therefore,the price function of the option can be written as follows:p=f(St,K,T,r,a).In the pricing model of options,the most important is the Black-Scholes mod-el,which is the standard model of European option pricing.The most important assumption in the B-S model is that the volatility is constant.This paper gives a detailed mathematical derivation process of the B-S model formula,as well as the option price formula with dividends.However,certain improvements to the B-S model can make it suitable for American option pricing in some cases.Since the Black-Scholes model considers the volatility constant,this is incon-sistent with what we observed in real life,so Heston proposed a new option pricing model in 1993——the Heston model.The target asset volatility in the model is in line with the CIR process,and the volatility is also considered to be random,which makes the obtained option price more in line with the actual market.The actual historical data shows that for different option durations,it does not have a good one-to-one correspondence with the single volatility model.Therefore,different volatility is determined in the model according to different time periods.Based on the above situation,this paper gives a new model,which not only con-siders the situation of stock allocation but also considers the influence of different stochastic volatility.The model is roughly divided into two time periods,which are divided according to the timing of the allotment.In the time period before the allotment,the volatility of the interest rate in the Vasicek model is used to de-scribe the volatility of the stock price.The CIR random interest rate model adopted during the post-allotment period is used to characterize the volatility during that period.Because this paper believes that the single consideration of volatility in an option pricing model is somewhat biased towards the outcome of the option price,the two volatility factors considered in this paper will make the considerations more comprehensive,and the improvement is more relevant to the actual situation.This paper briefly introduces the Vasicek model and the CIR model and gives the par-tial differential equation that the option price should satisfy in two time periods.The derivation process is given for the European call option price formula with the volatility satisfying the CIR model.