基于USV 特征的商品期货期权定价理论及实证研究

WuYang

摘要
通过对市场交易数据进行分析，我们发现市场波动具有 USV（Unspanned Stochastic Volatility）特征。因此，我们运用基于不可生成的波动性存在假设的更优化的期权定价模型对期权进行定价。在实证研究中，本文利用2009 年2 月17日至2011 年7 月12 日的 COMEX 黄金期货期权的数据，运用扩展的卡尔曼滤波方法结合拟极大似然函数法得到其待估参数，并对样本外时间点的期权定价进行了预测并将USV 模型与其他三个（Merton，Bates，Crosby）经典模型的预测效果进行比较。从误差均值、误差标准差、误差最大值三个指标来看，基于USV修正后的期权定价效果并不比Merton、Bates 和Crosby 的模型更好，即不同于经典文献的记录，我们进行的基于USV 视角的期权定价模型效果一般。与此同时，USV 的运算过程非常复杂，计算机处理时间很长，运算效率尚没有达到实务中运用的要求。因此，从定价效果和效率来看，运用基于USV 的假设来指导商品期货期权的定价模型还需要不断完善。

关键词：USV 模型，卡尔曼滤波，拟极大似然函数

Abstract

After analyzing the market trading data, we find out that option pricing has the Unspanned Stochastic Volatility character. Therefore, we revised option pricing model based on the USV assumption and use it in the pricing work. We use COMEX Gold’ data to do the empirical analysis; the sample period is from Feb. 17, 2009 to Jul. 12, 2011. Besides, we also use Merton, Bates and Crosby’s option pricing model to do the empirical analysis and then compare the effect and the efficiency of the above four option pricing models. Although the calculating procedure of USV model is much more complicated and time-consuming, the revised option pricing model based on the USV assumption is no better than the Merton, Bates and Crosby’s models. Therefore, the revised option pricing model based on USV assumption needs further improvement, in terms of both pricing effect and efficiency.

Key Words: USV model, Kalman filtering, Quasi-maximum likelihood function