Abstract: Dynamic pricing of European options involves the repeated dynamics of price observation, model choice, state variable estimation, and option pricing for the next time grid. To function well, an approach to dynamic option pricing has to be sequential, accurate, and easy to apply. This paper, therefore, proposes an approach to dynamic pricing based on Hull-White extensions. Specifically, the time-homogeneous affine stochastic volatility model is adopted as the basic model for Hull-White extension. In markets where only a limited number of options exist, instantaneous variance is estimated using the particle filter algorithm, and the Hull-White extension for pricing is updated without changing explicit parameters, both according to the observed option pricing surface. Pricing is further realized using forward characteristics. The results of empirical tests show that compared with the normal risk neutral pricing based on competing models, both with constant model parameters and with parameter learning, the approach proposed in this paper significantly improves the accuracy and stability of pricing results.

Key words: dynamic option pricing, Hull-White extension, option price surface, affine stochastic volatility model, particle filter

摘要： 欧式期权的动态定价过程可归结为：实际价格观测、模型选择、状态变量估计以及下一时刻期权定价的动态循环。为使这一定价过程兼具序贯性、准确性及易行性，设计了一种基于Hull-White扩展模型的动态定价方法：以平稳仿射随机波动率模型作为基础模型，在仅存有限个期权合约时，根据实际期权价格曲面，使用粒子滤波方法估计瞬时方差，并在固定显式参数下，更新Hull-White扩展模型；进而利用前向特征过程，实现下一时刻的期权定价。实证表明：相比于固定参数及参数学习下基于对比模型的一般风险中性定价，使用基于Hull-White扩展模型的动态定价方法时，期权定价准确性和稳定性均显著提升。

关键词: 期权动态定价, Hull-White扩展模型, 期权价格曲面, 仿射随机波动率模型, 粒子滤波