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为了研究Knight不确定环境下Lévy型金融市场中的期权定价,假设标的资产的价格服从Lévy过程,建立了Knight不确定环境下期权的动态定价模型以及欧式期权的最小定价模型,并借助等价概率测度、倒向随机微分方程(backward stochastic differential equation,BSDE)等理论分别求出了模型的显示解。最后,利用数值分析方法,研究了Knight不确定性参数对欧式看涨期权价格的重要影响。结果表明:Knight不确定风险对欧式期权定价影响显著,随着Knight不确定参数的增加,欧式看涨期权的最小价格呈现递减的趋势,最终将趋于稳健。
In order to study the option pricing in Lévy-type financial market under Knight uncertainty, suppose the price of underlying asset obeys the Lévy process, and establishes the dynamic pricing model of options in Knight’s uncertain environment and the minimum pricing model of European options. With the help of equivalence probability Measure, backward stochastic differential equation (BSDE) and so on, respectively. Finally, numerical analysis is used to study the important influence of Knight uncertainty on the price of European call option. The results show that the uncertain risk of Knight has a significant impact on European option pricing. With the increase of Knight’s uncertain parameters, the minimum price of European call options tends to decrease and will eventually stabilize.