Functional Vašiček Model
将经典Vašiček模型扩展到函数型数据分析框架，把每个交易日内的连续利率视为一个统计对象，估计日内时变的波动率和回复率参数，对金融利率建模者有用。
ABSTRACT We propose a new formulation of the Vašičekmodel within the framework of functional data analysis. We treat observations (continuous‐time rates) within a suitably defined trading day as a single statistical object. We then consider a sequence of such objects, indexed by day. In addition to the common long‐term rate, the objects are parametrized by two functional parameters, the volatility curve and the reversion curve, which replace analogous scalar parameters in the classical Vašičekmodel. Such a modeling paradigm allows us to estimate instantaneous reversion and volatility parameters within a trading day, thus allowing them to evolve with the time of day. The model is estimated within a new framework that combines techniques of functional data analysis with those of SDEs. In particular, large sample properties are derived as the number of days and the number of discrete time points at which the rate curves are observed tend to infinity.