考虑微观结构噪声的非仿射期权定价研究——基于上证50ETF期权高频数据的实证分析

Non-affine Option Pricing in the Presence of Microstructure Noises:An Empirical Study Based on the High-frequency Shanghai 50ETF Options Data

考虑了存在市场微观结构噪声情形下基于非仿射随机波动率模型的上证50ETF期权的定价问题.首先,基于幂级数展开方法得到了非仿射随机波动率模型下欧式期权的近似定价公式;其次,运用卡尔曼滤波对观测的上证50ETF价格中的微观结构噪声进行过滤,得到了上证50ETF有效价格,进而采用上证50ETF有效价格与iVX波动率指数数据,建立了基于有效重要性抽样的极大似然(EIS-ML)估计方法,对非仿射随机波动率模型的客观与风险中性参数进行了联合估计;最后,采用上证50ETF期权5分钟高频交易数据进行了实证研究.结果表明:微观结构噪声会对期权定价产生重要的影响,考虑微观结构噪声能够改进模型的期权定价表现;无论考虑微观结构噪声与否,非仿射随机波动率模型都比Black-Scholes模型具有更高的定价精确性,表明非仿射波动率能够改进期权定价表现;未考虑微观结构噪声的非仿射随机波动率模型相比考虑微观结构噪声的Black-Scholes模型具有更高的定价精确性,表明非仿射波动率相比微观结构噪声对于期权定价具有更大的影响.

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 50 ETF options is considered under the non-affinestochastic 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 50 ETF prices are filtered.Then based on the data of the filtered Shanghai 50 ETF 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 50 ETF 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.