I'm implementing a lot of stochastic models on my own for fun and I'm quite puzzled about the usual procedure concerning the correctnes of Bermudan swaptions prices and greeks ? How can you tell that the price that you get from the implementation/model is correct?
Should I price the same instrument using the same model but different methods (MC, PDE, Trees) ?
Should I price the same instrument using different models and if they look similar it means that the price is correct ?
Should I try to price degenerate cases of Bermudan swaptions like bermudan swaptions with strike 0 and just see if the model behaves as expected ? I would usually go for this one but I feel that it's not enough, i may be wrong.
I tried to do some research on the case, but didn't found much even when reading some Model Risk Management books. If possible could you also please provide some litterature ?