Break-even volatility for caps, floors and swaptions

Abstract

This dissertation investigates break-even volatility in the context of the South African interest rate market. Introduced by Dupire (2006), break-even volatility is a retrospective measure defined as the volatility that ensures the profit or loss from a delta hedged option position is zero. Break-even volatility sheds light on the inner structure of the market and is a promising investigatory tool. Insurance houses in South Africa are interested in modelling long-dated interest rate derivatives embedded within their liabilities. In pursuit of this goal, some are currently calibrating the Lognormal Forward-LIBOR Market Model to market prices. They rarely directly trade in said derivatives, but merely delta hedge their risk daily. In this case, break-even volatility surfaces become more relevant than recovering market prices (which incorporate the banks risk premium and profit margin) as it should better represent the historical cost of replicating the option under consideration. This dissertation ultimately assesses the use of the Lognormal Forward-LIBOR Market Model in the South African interest rate market using break-even volatility. It is found that several caps and swaptions are trading at volatilities that differ significantly from their break-even volatility estimates. Furthermore, through an investigation into the calibration of the Lognormal Forward-LIBOR Market Model to break-even volatilities, an argument that the underlying dynamics of the model are incompatible with that of the South African interest rate market is developed.