This paper evaluates the improvement in option pricing brought about by realized volatility (RV) through nonaffine dynamics as advocated by Christoffersen et al. (2014). We complement their studies by developing a closed-form approximation of option pricing for the nonaffine models with RV, and then study the trade-off between the degradation in data fitting and the computational convenience offered by the analytical formula. Our studies confirm the literature that the nonaffine dynamics consistently outperform the affine in option pricing. In particular, we find that RV can significantly improve return fitting and option pricing through both affine and nonaffine models. For the affine models, we find strong evidence in favor of the RV information for both returns and options; for the nonaffine models, the evidence is less convincing for option pricing. We also provide additional new evidence that RV and nonaffine structures are equally competent at improving option pricing; moreover, these two features are complements rather than substitutes for GARCH option pricing, and the importance of one feature for option pricing is further enhanced when the other is present. All of these results are robust across moneyness, maturity, and volatility levels, and point to the necessity of including RV in nonaffine option pricing models.

中文翻译：

---

通过非仿射动力学和已实现波动率进行期权估值

本文评估了 Christoffersen 等人所倡导的通过非仿射动力学实现的波动率 (RV) 带来的期权定价改进。 （2014）。我们通过为具有 RV 的非仿射模型开发期权定价的封闭式近似来补充他们的研究，然后研究数据拟合的退化与分析公式提供的计算便利性之间的权衡。我们的研究证实了文献表明，非仿射动力学在期权定价方面始终优于仿射动力学。特别是，我们发现 RV 可以通过仿射和非仿射模型显着改善收益拟合和期权定价。对于仿射模型，我们发现了强有力的证据支持收益和期权的 RV 信息；对于非仿射模型，期权定价的证据不太有说服力。我们还提供了额外的新证据，证明 RV 和非仿射结构在改善期权定价方面同样有能力；而且，这两个特征是 GARCH 期权定价的补充而不是替代，当其中一个特征存在时，另一个特征对于期权定价的重要性会进一步增强。所有这些结果在货币性、成熟度和波动性水平方面都很稳健，并表明有必要将 RV 纳入非仿射期权定价模型中。