Modeling Multiple Ibor Curves and Stochastic Basis Spreads

Summary

The discussion considers how to extend an interest-rate model calibrated to six-month EURIBOR to other tenors and an overnight index while accommodating negative rates. It frames two choices: model each index separately with a two-factor Gaussian short-rate model, or represent differences between index curves through basis spreads. The response suggests starting with a deterministic basis spread and notes that research has modeled spreads as separate positive stochastic processes or modeled the indices directly.

A central modeling concern is that independently simulated curves may cross, producing tenor orderings the author considers undesirable. The answer agrees that preventing such twists can be difficult when modeling the indices directly. It points to prior literature on basis modeling and cautions that basis spreads can be negative in observed markets, so imposing positivity may not fit all conditions. The excerpt gives no calibrated specification, equations, implementation details, or empirical comparison; it is guidance on modeling choices rather than a complete model.

Key ideas

• A deterministic basis spread is offered as a possible initial modeling approach.
• Basis spreads can be modeled as separate stochastic processes or through models of the indices themselves.
• Modeling each index independently can allow simulated curves to cross and create unwanted tenor twists.
• Negative basis spreads have been observed, so a model should not assume they are always positive without justification.
• The discussion points to prior basis-modeling research but does not specify a complete calibration or simulation procedure.

Tags

# Negative Interest Rate & Basis Models


# Negative Interest Rate & Basis Models












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 by jimifiki (score 2)

https://quant.stackexchange.com/a/18295

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.

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