Abstract

Based on the fact that realized measures of volatility are affected by measurement errors, we introduce a new family of discrete-time stochastic volatility models having two measurement equations relating both observed returns and realized measures to the latent conditional variance. A semi-analytical option pricing framework is developed for this class of models. In addition, we provide analytical filtering and smoothing recursions for the basic specification of the model, and an effective MCMC algorithm for its richer variants. The empirical analysis shows the effectiveness of filtering and smoothing realized measures in inflating the latent volatility persistence—the crucial parameter in pricing Standard and Poor’s 500 Index options.

摘要

基于已实现的波动率测量值受测量误差影响这一事实，我们引入了一个新的离散时间随机波动率模型系列，该模型具有两个将观测到的收益和已实现的测量值与潜在条件方差相关的测量方程。针对此类模型开发了半分析期权定价框架。此外，我们为模型的基本规范提供了分析滤波和平滑递归，并为其更丰富的变量提供了有效的MCMC算法。实证分析表明，过滤和平滑已实现的措施可以有效地提高潜在波动率的持续性，这是定价标准和普尔500指数期权中的关键参数。