**Zhe Li**

Business School, Nanjing Normal University, Nanjing 210023, China; zheli@njnu.edu.cn

Received: 21 November 2019; Accepted: 12 January 2020; Published: 17 January 2020

**Abstract:** Recently, a large number of empirical studies indicated that individual equity options exhibit a strong factor structure. In this paper, the importance of systematic and idiosyncratic volatility and jump risks on individual equity option pricing is analyzed. First, we propose a new factor structure model for pricing the individual equity options with stochastic volatility and jumps, which takes into account four types of risks, i.e., the systematic diffusion, the idiosyncratic diffusion, the systematic jump, and the idiosyncratic jump. Second, we derive the closed-form solutions for the prices of both the market index and individual equity options by utilizing the Fourier inversion. Finally, empirical studies are carried out to show the superiority of our model based on the S&P 500 index and the stock of Apple Inc. on options. The out-of-sample pricing performance of our proposed model outperforms the other three benchmark models especially for short term and deep out-of-the-money options.

**Keywords:** equity option pricing; factor models; stochastic volatility; jumps

**JEL Classification:** G13
