Abstracts

We explore the low variance martingale (LVM) assumption and their implications. LVM assumption was proposed by Schrager and Pelsser (2006) for pricing interest rate derivatives, in particular swaptions, under affine term structure models (ATSMs). A similar assumption is also used in LIBOR market model (LMM) and it is usually known as freezing the drift. Once the method based on LVM assumption is easy and has an intuitive implementation it has been preferred by practitioners.
The LVM assumption assumes that the ratio between a zero coupon bond and a portfolio of discount bonds (based on a specific tenor) is a low variance martingale under the swap measure. So, their value at each time may be approximate by its conditional expected value, particularly by their time zero value.
We prove that the LVM assumption implies that the instantaneous forward rates are frozen at their initial values. Based on this consequence, we deduce the parameters values at each time for Nelson-Siegel and Svensson models.
We also provide an empirical study, based on real financial market. We use data available at European Central Bank (ECB). Hence, we investigate the periods where the LVM assumption is acceptable and the periods where there are substantial differences. Finally, we compare these periods with the global economic environment.