固定执行价格下回望看涨期权保险精算定价

An Actuarial Option Pricing Approach to European Fixed Strike Lookback Call Option

利用保险精算方法,将期权定价问题转化为纯保费确定问题,根据股票价格过程的实际概率测度推导出了无风险利率为常数时,固定执行价格下回望看涨期权定价公式,验证了当标的资产的期望收益率等于无风险利率时,保险精算定价和风险中性定价的一致性.最后通过实例分析了保险精算价格和风险中性价格的差异,并利用Matlab编程得到了保险精算价格与标的资产期望收益率之间的关系.

Using the actuarial option pricing approach,the option pricing problem was changed into a pure premium determination.This paper first deduced the pricing formula of the European fixed strike lookback call option by using the actuarial option pricing approach and the physical probabilistic measure of stock price process.With this result,it verifies that the actuarial option pricing is consistent with the risk neutral pricing when the expected rate of return of the asset equals the risk free rate.Then,the difference was compared between the two methods through numerical examples.Lastly,the relationship was derived between the actuarial approach price and the expected rate of return of the asset.