标题： 基于后验Cramer-Rao下界自适应状态估计的期权价格预测 显示英文标题

标题： Posterior Cramer-Rao Lower Bound based Adaptive State Estimation for Option Price Forecasting

摘要： 贝叶斯滤波在数学金融中已被广泛应用，主要应用于随机波动率模型。 它们有助于从观察到的市场数据中估计未观测到的潜在变量。 由于计算能力的提高以及模型参数估计和隐含波动率理论的研究增加，该领域近年来取得了巨大发展。 在本文中，我们设计了一种新方法，利用贝叶斯滤波理论和后验Cramer-Rao下界（PCRLB）从期权价格中估计底层状态（波动率和风险），并进一步用于期权价格预测。 几种贝叶斯滤波器，如扩展卡尔曼滤波器（EKF）、无迹卡尔曼滤波器（UKF）、粒子滤波器（PF）被用于在GARCH模型动力学下对Black-Scholes模型的潜在状态进行估计。 我们采用平均和最佳情况切换策略，对类似Black-Scholes的非线性、离散时间状态空间模型（SSM）进行自适应状态估计，使用基于PCRLB的性能度量来判断每一步的最佳滤波器[1]。 由于估计PCRLB的闭式解并不容易，我们采用基于粒子滤波器的PCRLB近似方法，参考[2]。 我们在来自S$\&$P 500的期权数据上测试了我们提出的框架，从实际期权价格中估计底层状态，并用来估计期权的理论价格和预测未来价格。 我们提出的方法比用于估计底层状态的单独应用滤波器表现要好得多，并显著提高了预测能力。 显示英文摘要

摘要： The use of Bayesian filtering has been widely used in mathematical finance, primarily in Stochastic Volatility models. They help in estimating unobserved latent variables from observed market data. This field saw huge developments in recent years, because of the increased computational power and increased research in the model parameter estimation and implied volatility theory. In this paper, we design a novel method to estimate underlying states (volatility and risk) from option prices using Bayesian filtering theory and Posterior Cramer-Rao Lower Bound (PCRLB), further using it for option price prediction. Several Bayesian filters like Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF), Particle Filter (PF) are used for latent state estimation of Black-Scholes model under a GARCH model dynamics. We employ an Average and Best case switching strategy for adaptive state estimation of a non-linear, discrete-time state space model (SSM) like Black-Scholes, using PCRLB based performance measure to judge the best filter at each time step [1]. Since estimating closed-form solution of PCRLB is non-trivial, we employ a particle filter based approximation of PCRLB based on [2]. We test our proposed framework on option data from S$\&$P 500, estimating the underlying state from the real option price, and using it to estimate theoretical price of the option and forecasting future prices. Our proposed method performs much better than the individual applied filter used for estimating the underlying state and substantially improve forecasting capabilities.