OIS DISCOUNTING, INTEREST RATE DERIVATIVES, AND THE MODELING OF STOCHASTIC INTEREST RATE SPREADS

John Hull and Alan White

Before 2007, derivatives practitioners used a zero curve that was bootstrapped from LIBOR swap rates to provide “risk-free” rates when pricing derivatives. In the last few years, when pricing fully collateralized transactions, practitioners have switched to using a zero curve bootstrapped from overnight indexed swap (OIS) rates for discounting. This paper explains the calculations underlying the use of OIS rates and investigates the impact of the switch on the pricing of plain vanilla caps and swap options. It also explores how more complex derivatives providing payoffs dependent on LIBOR, or any other reference rate, can be valued. It presents new results showing that they can be handled by constructing a single tree for the evolution of the OIS rate.