Forward Rate Volatilities, Swap Rate Volatilities, and the Implementation of the Libor Market Model

This paper presents a number of new ideas concerned with the implementation of theLIBOR market model and its extensions. It develops and tests an analytic approximationfor calculating the volatilities used by the market to price European swap options fromthe volatilities used to price interest rate caps. The approximation is very accurate forthe range of market parameters normally encountered and enables swap option volatility skews to be implied from cap volatility skews. It also allows the LIBOR market model to be calibrated to broker quotes on caps and European swap options so that other interest rate derivatives can be valued