基于混合卡尔曼粒子滤波算法的期权定价方法

Option pricing based on mixture Kalman particle filter

针对金融领域的期权定价问题,为提高粒子滤波算法对期权价格的估计精度,提出使用混合卡尔曼粒子滤波算法(MKPF)进行期权价格预测,该算法使用Unscented卡尔曼滤波器和扩展卡尔曼滤波器作为混合建议分布产生重要采样密度。在某一时刻,每一个粒子首先经过Unscented卡尔曼滤波器更新得到一个状态估计值,然后以该估计值作为扩展卡尔曼滤波器的先验估计再次更新粒子,得到该时刻最终的估计值。实验中针对经典的Black-Scholes期权定价公式,使用包括MKPF算法在内的4种算法对期权价格进行预测,结果表明MKPF算法预测的期权价格与真实期权价格的误差最小,证明了MKPF算法在期权定价问题中的有效性。

In order to improve the estimation performance of particle filters in option pricing, a method, called Mixture Kalman Particle Filter （MKPF）, was used to solve the problems. The MKPF used Unscented Kalman Filter （UKF） and Extended Kalman Filter （EKF） as mixture proposal distribution. At certain time, each particle was firstly updated by the UKF to get a state estimation; thereafter, this estimation was used as the prior of the EKF, in which the particle was updated again to gain the final estimation of the state. The authors used the classical Black-Scholes （B-S） model in the experiment in order to evaluate the performance of the newly proposed method. The experimental results show that the MKPF outperforms other algorithms, which shows the validity of the MKPF algorithm in option pricing.