Expected and Unexpected Jumps in the Overnight Rate: Consistent Management of the Libor Transition

Interest-rate benchmark reform has revived short-rate modelling. One reason is that short-rate models provide a consistent framework in which different benchmarks, and contracts linked to them, can be compared. Another reason is that new benchmarks can be directly dependent on very short-term rates; the key example is a backward-looking compounding of overnight rates, a prominent alternative to forward-looking Libor. Indeed, under Libor, one can often safely ignore aspects of short-rate behaviour, especially jumps. At least partially for this reason, jumps are inadequately treated in the interest-rate literature, particularly expected jumps (jumps with known timing). We estimate a model with expected and unexpected jumps, which involves separating their effect on term rates. We then price forward- and backward-looking caplets, quantifying the spread exhibited by the latter over the former. Expected jumps lead to significantly time-inhomogeneous option behaviour, particularly for short-term options linked to a backward-looking benchmark.