When calculating XVA or Counterparty Credit Risk (CCR), you can choose to simulate your interest rate with a Multi-factor interest rate model or a Single-factor interest rate model.

What are the pros and cons of using a Multi-factor interest rate model over a Single-factor interest rate model?


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As you may know, XVA and CCR computations are complex and involve a huge Monte Carlo with a multi-asset diffusion, netting of trades, etc.

Simplicity and better (computational) performance

On the one hand, using a single-factor model means more simplicity and a better performance, this can be very important for example if one has real-time limits on the PFE for counterparty credit risk control, or is computing very computationally-intensive XVAs (e.g. MVA, KVA taking into account CVA capital risk charge, etc.).

Some risks are not captured

On the other hand, a single-factor model will basically simulate only parallel shifts of the curve. This is not enough if you are sensitive to a change in the slope of the curve, which will be the case for realistic portfolios.

In such a case, you would be underestimating your CCR by using a single-factor model.

PCA studies show that 3 factors usually capture more than 90% of curve deformations, and that 2 factors usually capture more than 80%. So, I would say that a 2 factor model provides a good balance between simplicity/performance and risk explanation.


There are other point that could come into play depending on what you want to do. Let us consider the calibration of your model for example. If you want to match a large set of calibration instruments, then you will likely not be able to do it with a single factor model.


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