Knight不确定环境下由Lévy过程驱动的期权定价

Option pricing under Knight uncertainty driven by Lévy process

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。

To deal with option pricing under Knight uncertainty in Levy financial market, assuming the underlying stock asset fol-lows Levy process？ the supper and lower bounds model and the minimal pricing of European options are established. Moreover, the explicit solutions of the above two models were given by using the equivalent probability martingale measure and the theories of backward stochastic differential equation （BSDE）. Finally, the important impact of Knight uncertainty on the pricing of Euro-pean call options was studied through numerical analysis. Results show that knight uncertainty risks have significant impact on the pricing of European options. With the increase of Knight parameter, the minimal pricing of European call options become smaller and smaller, and will become stable eventually.