基于Black-Scholes模型的期权定价新方法

摘要

考虑到实际金融市场的不完备性以及收益率分布的厚尾性,基于经典Black-Scholes模型并运用函数的下凸性,期权定价公式H（a）=E[（X-a）2]被推广为Hk（a）=E[（X-a）2k].通过DJSH（道琼斯上海）指数收益率的GARCH模型,并使用随机模拟的方法对这两个公式进行定价比较.结果表明这种方法有效提高了定价,从而降低了风险.%Actual financial markets are incompleted and distributions of yield rate are fat-tailed,so based on the classical Black-Scholes model and using downward convex property of function,option pricing formula H（a）=E[（X-a）2] is generalized to Hk（a）=E[（X-a）2k].With the GARCH model of DJSH rate and by using the method of stochastic simulation,effects of the two pricing formulas are compared.The results show that the new formula of option pricing effectively increases the price and reduces the risk.