波动率估计是金融学的核心, 波动几乎渗透金融市场的每一个领域. 为了快速而精确地提取波动率, 文章将比例UT变换与最小偏度单行采样技术和无迹卡尔曼滤波(UKF)算法相结合, 提出一种适用于非线性高斯状态空间模型的改进的无迹卡尔曼滤波(MUKF)算法, 并将该算法应用到扩散的期权定价模型中. 最后 通过对Heston随机波动模型进行模拟研究, 发现在同时使用股票价格数据和期权 数据时, 可以精确地提取波动率, 而且MUKF算法比UKF算法的计算时间更短. 文章也对Heston模型中的波动率的波动参数进行了研究, 研究发现MUKF算法可以准确地 捕捉这种波动率特性.

As volatility pervades almost everywhere in financial markets, its estimation has become one of the key points in financial economics. In order to capture the volatility dynamics accurately and quickly, this paper combines the unscented transformation, the minimum of skewness single sampling strategy with the unscented Kalman filter (UKF) algorithm to propose a modified unscented Kalman filter algorithm for nonlinear Gaussian system. The algorithm is applied to volatility extraction in a diffusion option pricing model. Simulation study with the Heston stochastic volatility model indicates that to obtain an accurate estimation of volatility, both the stock and option prices are necessary, and the computation time of MUKF is less than UKF algorithm. This paper also studies the volatility of volatility parameter in the Heston model and indicates that MUKF algorithm can govern the variation of volatility.