Non-recombining trinomial tree pricing mode and calibration for the volatility smile

作者：Gong, Wenxiu; Xu, Zuoliang^*

来源：Journal of Inverse and Ill-Posed Problems, 2019, 27(3): 353-366.

DOI：10.1515/jiip-2018-0005

• Volatility
• non-recombining trinomial tree model
• option pricing
• calibration
• nonlinear unconstrained optimization

In this paper, we consider the non-recombining trinomial tree pricing model under the volatility, which is a function of time, establish the option pricing model and give the convergence rates of the non-recombining trinomial tree method. In addition, we research the calibration problem of volatility and adopt an exterior penalty method to transform this problem into a nonlinear unconstrained optimization problem. For the optimization problem, we use the quasi-Newton algorithm. Finally, we test our model by numerical examples and options data on the S&P 500 index. The results show the effectiveness of the non-recombining trinomial tree pricing model.

• 出版日期2019-6
• 单位中国人民大学