灰色模糊环境下基于跳扩散过程的脆弱期权定价模型

Vulnerable Option Pricing Model Based on Jump-diffusion Process under Grey Ambiguity

对期权定价管理中大量非精准的不确定性决策,本文将灰色模糊理论引入到传统期权定价模型中,构建了灰色模糊环境下基于跳扩散过程的欧式脆弱期权定价模型(GFL模型)。将无风险利率、收益率、波动率等市场参数假定为灰色模糊数,并重新定义了该模型中灰色模糊可能性均值、灰色模糊核、基于灰色模糊核的模糊白化域等概念。而后,通过实证分析对不确定性环境下,灰色模糊数的灰度对灰色模糊核及模糊白化价格域的影响进行了研究。结果表明,灰色模糊环境下基于跳扩散过程的脆弱期权定价模型,能够根据投资者掌握信息的程度,确定期权的核心参考价格及参考价格区间,更好地引导投资者做出更有效地投资决策。

This paper introduces gray ambiguity theory into the traditional option pricing model for a large number of uncertain decision-making in option pricing problem.Based on jump-diffusion process in gray ambiguous environment,the paper assumes market parameters as grey fuzzy number,such as the risk-free interest and rate of return,to construct a GFL model for pricing the European vulnerable options.Besides,concepts such as gray fuzzy likelihood average,gary fuzzy kernel,and fuzzy whitening domain based on gary fuzzy kernel are redefined.Finally,the empirical analysis results illustrate the application of GFL model.We analyze the impact of the degree of grey ambiguity to the grey fuzzy price kernel and the fuzzy whitening price domain under uncertain environment.The results shows that the vulnerable option pricing model based on jump-diffusion process under grey ambiguity can determine the core reference price and a range of price according to the degree of investors’ grasping information,which could guide the investors to make more effective investment decision.