Explicit Computation of the Post-crisis Spot LIBOR in a Jump-Diffusion Framework

Starting from the worldwide financial crisis originated by the dramatic US economic events happened in 2007, many markets have seen a sudden growth of heterogeneous risk types, spanning from credit ones to liquidity ones. These abrupt changes in fundamentals, have produced the develop of significant spreads between the same interbank rate, e.g. the LIBOR rate, considered at different tenors. In the present chapter, we show how to explicitly compute the post-crisis spot LIBOR at different tenors, taking into account the possibility of jumps in the instantaneous spot rate trajectories, representing, in our setting, the so called OIS short-rate. Such an analysis is based on the intensity approach, where large and sudden movements can be modeled by adding marked point processes to the classical diffusion interest rate framework. Rigorous computations are also provided according with appropriate assumptions on the jumps intensity shape.