A Libor market model with a stochastic basis

The advent of the financial crisis made the previously negligible bases between different overnight interest rates explode. Fabio Mercurio adapts the classic Brace-Gatarek-Musiela Libor market model to the multiple curve environment, and shows how to price interest rate derivatives based on single or multiple Libor tenors under general stochastic volatility dynamics

The 2007 credit crunch brought unprecedented levels and volatility of basis spreads in the interest rate market. Classic no-arbitrage rules broke down and rates that used to closely track each other suddenly diverged. Discrepancies between theoretically equivalent rates were present in the market even before 2007. For instance, deposit rates and overnight indexed swap (OIS) rates for the same maturity had always been a few basis points apart. Likewise, swap rates with the same maturity, but