Valuing Interest Rate Swaps Using OIS Discounting

The financial crisis of 2007-09 precipitated a significant change in the practice of interest rate swap valuation. Going from traditional LIBOR to OIS (overnight indexed swap) discounting might not seem to be a profound event but it is more than just another method to calculate fair values for over-the-counter derivative contracts. It embodies newfound appreciation of counterparty credit risk and the role of collateral and central clearing. Implementation of OIS discounting has created a cottage industry for risk management consultants and trainers to deal with the technicalities of the new approach. From my academic perspective, it is clear that many of our finance textbooks that cover interest rate swaps need to be revised.The first section of this note reviews interest rate swap valuation in principle, the reasons for the move from LIBOR to OIS discounting, the implications for swap rates, and the 'winners and losers' that arise from the transition. The second section works through a numerical example to illustrate the calculations. This entails bootstrapping a sequence of discount factors that are consistent with interest rate swaps that have a market value of zero. The implied LIBOR forward curve is derived (or, in general, the forward curve for the money market reference rate). This curve becomes particularly important under OIS discounting when valuing a swap as a combination of fixed-rate and floating-rate bonds.Fortunately for risk managers, OIS discounting uses the same types of analytic techniques as the traditional approach. However, there are some differences that are beyond the scope of this note, for instance, calculating the sensitivities of swap values to changes in OIS rates and the LIBOR-OIS spread (i.e., working with dual curves rather than a single curve for risk measurement) and dealing with cross-currency swaps. Also, LIBOR is an interest rate that reasonably can be assumed to vary day by day in the interbank market whereas OIS rates are more directly a tool of monetary policy, suggesting that rate volatility depends on the pattern and timing of policy meetings and actions