Quantitative Finance underwent significant development over the past decade. For example, modelling of the term structure of interest rates after the GFC poses a unique challenge. The persistent phenomena of market basis spreads are an indication that markets are pricing various risks which are not captured in classical models. We pioneer a roll-over risk modelling framework to provide empirical evidence to the observed basis spreads, i.e., a spread between LIBOR of different tenors and LIBOR-OIS spread. This roll-over risk consists of two components, a credit risk component due to the possibility of being downgraded and thus facing a higher credit spread when attempting to roll over short–term borrowing, and a component reflecting the (systemic) possibility of being unable to roll over short–term borrowing at the reference rate (e.g., LIBOR) due to an absence of liquidity in the market. The modelling framework is of “reduced form" in the sense that the source of credit risk is not modelled (nor is the source of liquidity risk). We show how such model can be calibrated to market data, and used for relative pricing of interest rate derivatives, including bespoke tenor frequencies not liquidly traded in the market.
