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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.
Volatility estimation is the core of finance, and volatility permeates almost every area of the financial market.In order to extract volatility quickly and accurately, this paper combines proportional UT transform with minimum skewed single-row sampling technique and unscented Kalman filter (UKF) , An improved Unscented Kalman Filter (MUKF) algorithm is proposed for the nonlinear Gaussian state space model, and applied to the diffusion option pricing model.Finally, by simulating the Heston stochastic volatility model , We find that the volatility can be accurately extracted when the stock price data and the option data are used at the same time, and the MUKF algorithm is shorter than the UKF algorithm.The article also studies the volatility parameters of the Heston model, and finds that The MUKF algorithm accurately captures this volatility characteristic.