Functional Vašiček Model

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.