基于ARMA-GARCH调和稳态Levy过程的期权定价

通过收益率时间序列分析, 估计了非高斯ARMA-GARCH模型用以描绘资产价格的随机过程. 进一步假设模型的噪音分别服从标准正态分布及两类纯跳跃Levy分布 (经典调和稳态(CTS)和速降调和稳态(RDTS)), 并建立风险中性Levy-ARMA-GARCH模型进行恒生指数期权定价的实证研究. 研究结果表明: 中国股市主要股指的历史滤波噪音序列皆呈现尖峰有偏和肥尾的非高斯特征, 调和稳态相比其它Levy过程有更好的尖峰肥尾的刻画能力; 恒指价格的跳跃测度存在速降趋势, 形成收益率的尖峰厚尾; 布朗运动低估了金融市场震荡程度, 高斯分布高估短、中、长期隐含波动率; 调和稳态Levy过程的拟合与定价能力较好, 速降调和稳态过程综合的定价能力更稳健.

Option pricing based on ARMA-GARCH with tempered stable Levy processes

The historical filtering sequence of independent and identically distributed stationary noise was separated from the return rate of the HSI according to the autocorrelation and heteroskedasticity analysis. Assumed the noise obeys to normal, and two infinite pure jump of Levy processes — classical tempered stable (CTS) and the rapidly decreasing TS (RDTS), respectively this work studies the risk-neutral Levy-GARCH option pricing models. The results show that: Noise sequence has non-Gaussian characteristics, such as, skewed, peaking and having fat tail; tempered stable process has better fitting and pricing power than the normal; there is a trend of decreasing jump in asset pricing; Brownian motion underestimates the degree of financial market volatility and overestimates its short, medium and long-run model-inverted implied volatility; pricing power of RDTS process is more robust than TS process.