A New S.D.E. and Instantaneous Mean Reversion Rate Formula (Presented via a Numerical Empirical Model Comparison)

Abstract

The theory in this research is to ascertain that, not all models are good all the time. A comparison, of short-rate one factor models is calibrated and analyzed numerically via a Monte Carlo simulation, using two variance reduction techniques. The first technique is stratified sampling, the second the Sobol Algorithm. An empirical comparison is constructed using criterions of the goodness of fit of the models. The aim is to amend the discussion to ex-ante predictability of stochastic models. Five European exchange rates are examined. A new explicit instantaneous mean reversion formula and a new short rate model are introduced.