• 论文 •

### 跳-扩散模型下期权定价方法及参数校准

1. 1 中国人民大学数学学院 北京 100872
2 石家庄铁路职业技术学院 石家庄 050041
• 收稿日期:2017-12-28 出版日期:2019-06-26 发布日期:2019-06-27
• 通讯作者: 许作良 E-mail:xuzl@ruc.edu.cn
• 基金资助:
国家自然科学基金(11571365);国家自然科学基金(11401162);河北省高等学校科学技术研究重点项目(ZD2019080)

### Option Pricing Method and Parameter Calibration for Jump-Diffusion Model

Congcong Xu1,2,Zuoliang Xu1,*()

1. 1 School of Mathematics, Renmin University of China, Beijing 100872
2 Shijiazhuang Institute of Railway Technology, Shijiazhuang 050041
• Received:2017-12-28 Online:2019-06-26 Published:2019-06-27
• Contact: Zuoliang Xu E-mail:xuzl@ruc.edu.cn
• Supported by:
the NSFC(11571365);the NSFC(11401162);the Key Projects of Science and Technology Research in Colleges and Universities in Hebei Province(ZD2019080)

Abstract:

In this paper, the pricing method and parameter calibration of jump-diffusion model are investigated. First, the risk-neutral characteristic function of jump-diffusion model is derived under the mean correctiong equivalent martingale measure. The option under jump-diffusion model is priced by using the COS pricing method. Then, the pricing error of the COS algorithm is analyzed and the effectiveness of the COS pricing method is verified through numerical experiment. Subsequently, the parameters of the jump-diffusion model are calibrated by the relative entropy regularization method. Numerical experiments demonstrate the accuracy and reliability of the proposed method. Finally, the calibration method is tested by analyzing the S&P500 market data. The results show that the values of calibrated parameter are qualitatively for each maturity. Moreover, the results indicate a better fitting to the market data for the Merton jump-diffusion model in comparison to the Black-Scholes model.

• O211.6