I've only worked with RW model before but not RN interest rate models, so I'm looking for some practical insights on how RN calibration is done for interest rate models.
Let's say I want to start with a simple one year short rate model like CIR.
I could do the following:
- generate scenarios based on real world parameters
- assign weights to each scenarios
- optimize weights such that the difference between the one year forward curve from the market and the probability weighted average forward curve from the scenarios is minimized
The support for this approach is that real world and risk neutral scenarios don't have to be different in theory, and it's just the probability weights that are different between the two.
Alternatively, I could do:
- generate scenarios based on some random parameters as starting point
- calibrate the parameters in the model such that the simple average rates (equal weights among all scenarios) is close to the observable 1 year forward curve
Which one is more correct? I have a feeling that neither is correct. Practically, how is RN calibration done for interest rates models? What exactly are we calibrating to?
Also, in both methods above, all I model is the 1 year forward rates - is that enough? I can then calculate other forward rates based on what's implied in the 1 year forward rates.