Drift and volatility estimation in discrete time

Abstract In discrete time the increment of the logarithm of the price of a risky asset is supposed to involve two parameters which may be thought of as the ‘drift’ and ‘volatility’. It is assumed these parameters take finitely many values, and that they change value like a Markov chain on this state space. Filtering and parameter estimation techniques from Hidden Markov Models are then applied to obtain recursive estimates of the ‘drift’ and ‘volatility’. Further, all parameters in the model can be estimated. The method is illustrated by applying the results to two series of prices.