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.
Highlights
Most of the existing literature studies on option pricing are for index options, and there are very few about equity options
The results indicated that the equity options had a strong factor structure, and they developed an equity option pricing model with a capital asset pricing model (CAPM) factor structure and stochastic volatility, which allowed for mean reverting stochastic volatility for the dynamics of both the market factor and individual equity
The pricing performance of equity option valuation model considering market and idiosyncratic volatility and jump risks was significantly improved for short term and deep out-of-the-money (DOTM) options
Summary
Most of the existing literature studies on option pricing are for index options, and there are very few about equity options. Under the assumption that stock returns include a market component and an idiosyncratic component, Bakshi and Kapadia (2003b) developed a factor model for equity option valuation and investigated the pricing of market volatility risk in individual equity options. Their empirical results showed that volatility risk premiums in equity options are smaller than in index options. Afterwards, Fouque and Kollman (2011) proposed a continuous-time capital asset pricing model (CAPM) where the dynamics of the market index have a stochastic volatility driven by a fast mean reverting process.
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