关键词: 微观结构噪声, 非仿射波动率, 上证50ETF期权, iVX, 极大似然估计, 高频数据

Abstract: It has been well documented in the market microstructure literature that observed asset prices can diverge from their equilibrium values due to market microstructure noises (e.g. illiquidity, price discreteness and non-synchronous transactions). In markets where the microstructure noise effect is material, it will be ill-advised to ignore its presence. In the specific context of option pricing models, ignoring microstructure noise could non-trivially inflate one's estimate for the "true" asset volatility. Since the asset volatility plays a key role in the option pricing models, one is then likely to produce misleading estimates for option prices.
In the past two decades, the study of option pricing has made rapid development, which highlights the importance of stochastic volatility for option pricing. In particular, the affine stochastic volatility model has attracted a great deal of attention in the finance literature, because the model can provide computational tractability that leads to closed-form solution for European option. At the same time, many studies have found that the affine stochastic volatility model is not sufficient to describe the dynamics of the underlying asset and option prices, and provide strong evidence to support the non-affine stochastic volatility models, such as the GARCH diffusion model, which can characterize more realistic volatility paths and volatility distributions and significantly improving asset allocation and option pricing.
In this paper, the problem of the pricing of Shanghai 50ETF options is considered under the non-affine stochastic volatility model in the presence of market microstructure noises. Firstly, based on a power series expansion method, an approximation formula to price European options under the non-affine stochastic volatility model is obtained. Secondly, by applying the Kalman filter, the microstructure noises in the observed Shanghai 50ETF prices are filtered. Then based on the data of the filtered Shanghai 50ETF efficient prices and iVX volatility index, an efficient importance sampling-based maximum likelihood (EIS-ML) method is proposed to estimate jointly the objective and risk-neutral parameters of the non-affine stochastic volatility model. Finally, our model and approach is illustrated using 5-minute high-frequency data on the Shanghai 50ETF options. The empirical results demonstrate that the microstructure noises have an important effect on option pricing. The option pricing performance of the model can be improved when the microstructure noises are considered. The non-affine stochastic volatility model outperforms the Black-Scholes model regardless of whether the microstructure noises are considered, which implies that the specification of non-affine volatility plays an important role on option pricing. The non-affine stochastic volatility model without considering the microstructure noises outperforms the Black-Scholes model with microstructure noises, which demonstrates that the inclusion of non-affine volatility has a larger effect on option pricing than that of the microstructure noises.

Key words: microstructure noises, non-affine volatility, Shanghai 50ETF options, iVX, maximum likelihood estimation, high-frequency data