ANALYTICAL EVALUATION OF VOLATILITY FORECASTS*
针对连续时间随机波动率模型，利用特征函数方法推导了基于已实现波动率的简化形式预测效率的解析表达式，并评估了GARCH、多因子仿射和对数正态扩散等常见模型下该方法的相对表现。
Estimation and forecasting for realistic continuous‐time stochastic volatility models is hampered by the lack of closed‐form expressions for the likelihood. In response, Andersen, Bollerslev, Diebold, and Labys ( Econometrica , 71 (2003), 579–625) advocate forecasting integrated volatility via reduced‐form models for the realized volatility, constructed by summing high‐frequency squared returns. Building on the eigenfunction stochastic volatility models, we present analytical expressions for the forecast efficiency associated with this reduced‐form approach as a function of sampling frequency. For popular models like GARCH, multifactor affine, and lognormal diffusions, the reduced form procedures perform remarkably well relative to the optimal (infeasible) forecasts.