September 30th, 2003, 9:03 pm
As all of you know that one interesting features of interest rate products (instead of other ones as eg. Equities,etc. ) is the non- linear relation between the variation of Present value of such products and their yield. That relation is well known as convexity relation.(assuming that both are martingales exhibit inconsistency from mathematical point of view)Anyway, let's take a very simple example of a Libor-in-Arrear rate (set at time t_i and paid at the same time, which is different from its 'standard' definition set at begining at payd some time later t_(i+1). In the later 'natural' case the rate benefit from positive convexity relation, and as soon as the rate changes its features (in terms of payments), it changes its convexity 'exposure' loss (moving from longer maturity to shorter, eg. Libor/CMS in arrears etc.. ) or benefit in convexity (fixing at time t_i and payment at t_(i+2) instead of t_(i+1) for Libors).... This adjustment is known as 'convexity adjustment' aplied to IR rates, in order to be arbitrage-free ...........Hope it helps