广义Black-Scholes模型期权定价新方法--保险精算方法

利用公平保费原则和价格过程的实际概率测度推广了Mogens Bladt和Tina Hviid Rydberg的结果．在无中间红利和有中间红利两种情况下，把Black-Scholes模型推广到无风险资产(债券或银行存款)具有时间相依的利率和风险资产(股票)也具有时间相依的连续复利预期收益率和波动率的情况，在此情况下获得了欧式期权的精确定价公式以及买权与卖权之间的平价关系．给出了风险资产(股票)具有随机连续复利预期收益率和随机波动率的广义Black-Scholes模型的期权定价的一般方法．利用保险精算方法给出了股票价格遵循广义Ornstein-Uhlenback过程模型的欧式期权的精确定价公式和买权和卖权之间的平价关系．

New Method to Option Pricing for the General Black-Scholes Model-An Actuarial Approach

Using physical probability measure of price process and the principle of fair premium,the results of Mogens Bladt and Hina Hviid Rydberg are generalized.In two cases of paying intermediate divisends and no intermediate dividends,the Black_Scholes model is generalized to the case where the riskless asset (bond or bank account) earns a time_dependent interest rate and risky asset (stock) has time_dependent the continuously compounding expected rate of return, volatility.In these cases the accurate pricing formula and put_call parity of European option are obtained.The general approach of option pricing is given for the general Black_Scholes of the risk asset (stock) with a stochastic continuously compounding expected rate of return, volatility.The accurate pricing formula and put_call parity of European option on a stock whose price process is driven by general Ornstein_Uhlenback process are given by actuarial approach.