基于成分Realized EGARCH模型的期权定价研究

doi:10.16381/j.cnki.issn1003-207x.2022.1305

Abstract

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. It 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， the Component Realized EGARCH （CR-EGARCH） model is proposed， 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 the proposed CR-EGARCH model offers the best option pricing performance. Finally， it is confirmed 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

CLC Number:

F830.9

Xinyu Wu,Xuebao Yin,Haibin Xie, et al. Option Pricing with Component Realized EGARCH Model[J]. Chinese Journal of Management Science, 2026, 34(4): 22-33.

Figures/Tables 6

参数	EGARCH	C-EGARCH	R-EGARCH	CR-EGARCH
客观参数
$λ$	0.0270	0.0294	0.0305	0.0300
$λ$	(0.0066)	(0.0062)	(0.0036)	(0.0038)
$ω (m 1)$	-0.0797	-0.0214	-0.1216	-0.0766
$ω (m 1)$	(0.0008)	(0.0004)	(0.0013)	(0.0010)
$α 1$				0.1084
$α 1$				(0.0026)
$β 1$		0.9968		0.9910
$β 1$		(0.0001)		(0.0002)
$d 1$		0.0097		0.0109
$d 1$		(0.0030)		(0.0021)
$d 2$		0.0789		0.0388
$d 2$		(0.0033)		(0.0017)
$α (α 2)$			0.1372	0.0371
$α (α 2)$			(0.0025)	(0.0037)
$β (β 2)$	0.9892	0.9143	0.9857	0.7910
$β (β 2)$	(0.0003)	(0.0089)	(0.0002)	(0.0057)
$ν 1$	-0.0068	-0.0332	-0.0160	-0.0597
$ν 1$	(0.0027)	(0.0053)	(0.0019)	(0.0038)
$ν 2$	0.1574	0.1096	0.0527	0.0216
$ν 2$	(0.0032)	(0.0075)	(0.0016)	(0.0025)
$ξ$			-0.7385	-0.7376
$ξ$			(0.0030)	(0.0021)
$σ u 2$			0.4789	0.4743
$σ u 2$			(0.0092)	(0.0095)
$δ 1$			0.0628	0.0572
$δ 1$			(0.0039)	(0.0055)
$δ 2$			0.2575	0.2555
$δ 2$			(0.0032)	(0.0032)
波动率风险溢价
$χ$			0.1266	0.0748
$χ$			(0.0104)	(0.0101)
对数似然
$l n L R$	11530.5911	11542.8590	11577.6242	11581.3346
$l n L R, x$			7209.9617	7232.1409
$l n L O$			2526.1689	2700.0491

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价值状态	DTM < 30	30 < DTM < 60	60 < DTM < 120	DTM > 120	All
合约数目
S/K< 0.94	1417	1071	1376	1542	5406
0.94 <S/K< 0.97	508	456	432	659	2055
0.97 <S/K< 1.00	531	480	447	682	2140
All	2456	2007	2255	2883	9601
平均价格
S/K< 0.94	0.0043	0.0153	0.0324	0.0775	0.0345
0.94 <S/K< 0.97	0.0149	0.0379	0.0717	0.1196	0.0655
0.97 <S/K< 1.00	0.0338	0.0638	0.1030	0.1536	0.0932
All	0.0128	0.0320	0.0539	0.1052	0.0542
平均隐含波动率
S/K< 0.94	0.3528	0.2715	0.2627	0.2417	0.2821
0.94 <S/K< 0.97	0.2237	0.2075	0.2094	0.2014	0.2100
0.97 <S/K< 1.00	0.2066	0.2005	0.2020	0.1974	0.2013
All	0.2945	0.2400	0.2405	0.2220	0.2486

统计量	收益率	极差	对数极差
样本数	4123	4123	4123
均值	0.0003	0.0002	-9.2080
最小值	-0.1052	0.0000	-12.5720
最大值	0.0955	0.0073	-4.9171
标准差	0.0170	0.0004	1.1739
偏度	-0.1669	6.9482	0.2722
峰度	8.0099	79.6974	3.0168
Q(10)	38.6646	4265.4813	10273.9500

模型	B-S	EGARCH	C-EGARCH	R-EGARCH	CR-EGARCH
Overall IVRMSE	0.0729	0.0775	0.0614	0.0547	0.0473
IVRMSE by moneyness
S/K< 0.94	0.0750	0.0732	0.0599	0.0564	0.0473
0.94 <S/K< 0.97	0.0695	0.0723	0.0565	0.0485	0.0423
0.97 <S/K< 1.00	0.0707	0.0917	0.0692	0.0558	0.0515
IVRMSE by maturity
DTM < 30	0.0679	0.0613	0.0516	0.0666	0.0560
30 < DTM < 60	0.0716	0.0547	0.0464	0.0455	0.0425
60 < DTM < 120	0.0760	0.0672	0.0558	0.0450	0.0413
DTM > 120	0.0755	0.1058	0.0797	0.0561	0.0467

Option Pricing with Component Realized EGARCH Model

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