In this Element the authors review the technique of the change of numeraire in the martingale approach to option pricing. Their intention is to present a reader friendly explanation of the technique itself, and illustrate how it is applied in various fields of quantitative finance as the basis...

Using perturbation methods, approximate formulas are obtained for zero-coupon bonds under the generalized Black-Karasinski model. The formulas perform well regarding accuracy and calibration to available data. For a special case, which corresponds to the Hull-White model, the approximation...

A general procedure for creating Markovian interest rate models is presented. The models created by this procedure automatically fit within the HJM framework and fit the initial term structure exactly. Therefore they are arbitrage free. Because the models created by this procedure have only one...