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Hi Roland,

This is the LGM calibration, it looks like you are trying to calibrate both the model sigma and the mean reversion from a set of co-terminal swaptions, is that right? then you don’t have enough information to fully calibrate.

The functions in this context are the bootstrap helpers, which comes from the 11 swaptions that have been specified (by expiry and tenor).
The 12 available variables are the model variables (11 expiries and 1 mean reversion) or degrees of freedom if you prefer.