Solving the Puzzle in the Interest Rate Market

Abstract

Different anomalies have appeared in the interest rate market after the burst of the credit crunch. A wide wedge has opened between the market quotes of Forward Rate Agreements and their standard spot Libor replication, and large Basis Spreads have appeared for exchanging floating payments with different tenors. Here we tackle these issues under two aspects.In Part 1 we focus on issues of direct interest to market practitioners. We show that the gap between FRA rates and their spot Libor replication can be explained by using the quoted Basis spreads. Then we explain the market patterns of the Basis spreads by modeling them as options on the credit worthiness of the counterparty. We also investigate analytically the FRA market payoff.In Part 2 we study the mathematical representation of the interest rate market in the post-crisis reality. We introduce credit risk at market level, allowing for no-fault standard rule and collateralization. We use subfiltrations to model Libor rates, which now embed relevant credit risk although no default event is possible on Libor itself. We compute change of numeraire and convexity adjustments for collateralized derivatives tied to risky Libor.