Negative Interest Rate & Basis Models

Question

Since markets are showing negative interest rate, I'm forced to find a model that can catch this behaviour. Because of that, I have implemented and calibrated the G2++ (or the Hull-White 2 Factors) for the EURIBOR 6 Months.

The EURIBOR 6M has already been calibrated, but I also need to model the indexes EURIBOR OIS, EURIBOR 3M and EURIBOR 12M at the same time.

Do you know how to model these ibor indexes?

Shall I model the basis spread? or shall I implement also the G2++ for the rest of indexes?

If we implement the G2++ for the rest of indexes and we execute a Monte Carlo, we may get some trouble when indexes twist. I mean, in some cases EURIBOR 3M could become greater than EURIBOR 6M and theoretically it shouldn't be allowed.

Any idea about stochastic basis models?

Thank you very much in advance!

Answer 1

You can start with a deterministic basis spread.

There are several attempts to model the basis spread both modeling the spreads separately with positive stochastic processes and by modelling the different indexes. You are right: if you model the indices they could cross and it is hard to enforce abscence of twists.

Probably every paper on this subject cites Mercurio's seminal paper. Search your model in the papers citing Mercurio.

By the way, negative basis spreads have occasionally been observed.