A Consistent Stochastic Model of the Term Structure of Interest Rates for Multiple Tenors

Starting from economic first principles, i.e., the observation that single–currency swap basis spreads contradict classical arbitrage arguments, we construct a framework where this basis arises endogenously due to modelling of “roll–over risk.” This risk consists of two components: (1) Facing a higher credit spread (e.g. due to a credit downgrade) when rolling over short–term borrowing (2) Heightened borrowing costs due to an absence of market liquidity. The model simultaneously fits OIS, interest rate swap and basis swap market quotes. Including CDS market quotes allows the two components of roll–over risk to be explicitly separated. This is highly relevant to the current LIBOR transition, illustrating why alternative benchmarks are fundamentally different from the rates they may be replacing.