基于时变波动率的50ETF参数欧式期权定价

Parametric European Option Pricing of 50ETF Options Based on Time-varying Volatility

以上海证券交易所的首个股票期权品种50ETF为例,首先以时变波动率对经典BlackScholes期权定价公式常数波动率假设修正,然后基于正态分布、广义学生t分布和融入高阶矩的Edgeworth expansion渐近分布构建三种参数期权定价模型,最后采用参数显著性检验（Significance testing）、定价误差（Mispricing）、预测偏差（Forecastability）、对冲误差（Hedging errors）和波动率偏离修正（Volatility skew correction）5种严谨系统的评价标准,实证对比了在3种参数期权定价模型下的定价精度。研究结果表明：在时变波动率下,基于广义学生t分布和Edgeworth expansion渐近分布相比于正态分布显著提高了参数期权定价模型的定价精度。论文的研究成果为投资商和监管者提供了相对更为精确的期权定价模型。同时在相对更为准确的定价方法下,进一步利于50ETF期权在我国金融市场发挥价格发现和风险管理的作用。

In this paper, we first use the time-varying volatility to correct the constant volatility hypothe- sis in classical Black-Sholes option pricing model. Then, we construct three option valuation models under the normal distribution, generalized Student t-distribution and Edgeworth expansion approximating distribution. Last, treating the first stock option （50ETF） as empirical object, we compare these models＇ option pricing accuracy with five evaluation standards： significance testing, mispricing, forecastability, hedging errors, and volatility skew correction. The results prove that the time-varying volatility can improve the pricing accuracy clearly. Furthermore, compared with Black-Sholes option pricing model, the option pricing models with tilne-varying volatility and generalized Student t-distribution or Edgeworth expansion approximating distribution can yield iinprovements in the pricing of options. Thus, 50ETF can play the role of price discovery and risk management better with a more accurate option pricing methodology.