关键词: 期权定价, Realized EGARCH模型, 波动率成分, 杠杆效应, 极差

Abstract: Options are a type of financial derivative, which are mainly to be used as a tool for building investment strategies and managing financial risk. Options play an important role in developing the financial system, and generating economic growth. One of the important issues for trading options is to address the question on how options can be valued correctly. This paper aims to develop a reasonable model for pricing options. Classical option pricing model, such as the Black-Scholes (B-S) model, relies on the assumption that the underlying asset returns are normally distributed with constant volatility. However, the assumptions are inconsistent with empirical findings, resulting in option pricing biases and ``volatility smirk". It is well recognized that asset return distribution exhibits characteristics such as negative skewness and excess kurtosis. Moreover, asset returns exhibit volatility clustering, asymmetric volatility and long memory volatility behaviors. To overcome the drawbacks of the conventional option pricing approach, the GARCH option pricing models have been developed. However, the GARCH option pricing model fails to account for the intraday information as well as the complex volatility dynamics (such as asymmetric volatility and long memory volatility) for pricing options. In light of this, this paper proposes the Component Realized EGARCH (CR-EGARCH) model, which extends the Realized EGARCH (R-EGARCH) model through the incorporation of component volatility structure, to price options. The proposed CR-EGARCH model could more adequately capture the volatility dynamics, such as the long-memory volatility and the long-term and short-term leverage effects. Meanwhile, the model exploits the intraday information from realized measure, which is expected to improve return fitting and volatility estimates. The risk-neutral return dynamic is derived relying on the Radon-Nikodym derivative with dual shocks (return and volatility shocks). Using Monte Carlo simulation method, the prices for European options are computed. A sequential maximum likelihood estimation method is developed to estimate the parameters of the pricing model using data on the underlying asset and option prices. An empirical analysis based on Shanghai Stock Exchange (SSE) 50ETF options shows that in terms of implied volatility root mean squared error (IVRMSE) the CR-EGARCH model offers a 13.52% improvement over the standard R-EGARCH model. The R-EGARCH model offers 10.95%, 29.48% and 25.02% improvements over the Component EGARCH (C-EGARCH) model, the EGARCH model and the B-S model, respectively. The results provide strong support for incorporating the component volatility structure as well as the intraday extreme-value information from realized measure (range) to improve option pricing performance, with our proposed CR-EGARCH model offers the best option pricing performance. Finally, we confirm that the superior pricing performance of the CR-EGARCH model is robust to different evaluation criteria, different sample period, out-of-sample analysis, different realized measure and different option type.

Key words: option pricing, Realized EGARCH model, volatility components, leverage effects, range