Fixed Income Securities: Valuation, Risk, and Risk Management

Chapter 20

THE MARKET MODEL FOR STANDARD DERIVATIVES AND OPTIONS’ VOLATILITY DYNAMICS

In earlier chapters we covered standard derivatives, namely caps, floors, and swaptions, which make up a large fraction of the over-the-counter derivative securities market. In thischapter we review the quoting conventions used by market dealers to trade such securities. These quoting conventions rely on the use of a particular option pricing formula, the Blackformula, which was originally designed by Fischer Black to price options on commodityfutures. Although historically this formula was initially adopted by traders mainly for itssimplicity, and with the understanding that the formula has to be used as a simple wayto quote the prices of caps, floors, and swaptions, more recently it has been establishedthat this formula follows from a no arbitrage argument under some assumptions about thedynamics of stochastic variables.

We leave the derivation of this formula (and many others) to Chapter 21. In this chapter, instead, we take a more practical view and cover the market convention to quote caps, floors, and swaptions. For instance, Table 20.1 reports quotes for swaptions, caps andfloors on November 1, 2004 obtained from Bloomberg. Besides the swap rates in Column2, all of the quantities appearing in the table are expressed in volatility units. For instance, a 1-year cap was trading on November 1, 2004 at a 23.5% volatility, while a 2-year capwas trading at the much higher 29.89% volatility. Similarly, ...