A Stochastic Volatility Model With Realized Measures for Option Pricing

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.

鉴于已实现波动率测度（realized measures of volatility）存在测量误差这一现状，我们提出了一类全新的离散时间随机波动率模型。该模型包含两条测量方程，可将观测到的收益率与已实现波动率测度二者均与潜在条件方差建立关联。针对该类模型，我们构建了半解析期权定价框架。此外，我们针对该模型的基础设定推导了解析滤波与平滑递推公式，并为其更复杂的拓展形式设计了高效的马尔可夫链蒙特卡洛（MCMC）算法。实证分析表明，对已实现波动率测度进行滤波与平滑处理，能够有效提升潜在波动率持续性——该参数是标普500指数期权（Standard and Poor’s 500 Index options）定价的核心参数。