Given the multitude of existing interest rate models (ranging from simple to very complex) it would be interesting to know when the additional complexity actually makes sense.
The models I have in mind:
- Simple one factor (e.g. HW)
- Two factor models
- Two or one factor models with stochastic volatility
- LIBOR-Market, HJM, SABR and SABR-LMM model
Are there any rules of thumb to decide which model to use for which product? (Perhaps there is some book dealing with that topic that I am not aware of)
While trying to answer the question myself I found the follwing very interesting paper on the emperical comparison of interest rate models. Here the authors mainly compare how well the different models can fit market data and hit the relevant market pries after being calibrated.
Thus a follow up Question: (that is also related to the question on model validation)
Does it suffice to hit the market pries spot on after calibration for a model to qualify for being used in pricing for an instrument ? Or are there other aspects to be considered? (computational speed, statistical fittness, robustness of the hedges)
Let's assume my model fits the market data really well - backtesting however shows that the hedges it provides don't work that well. Also the model might not be able to statistially fit the path of the underlying. E.g. mean reversion can be observed in some markets but not in others. One could argue that risk neutrality does not necessarily entail meaningful real-world scenarios etc.
I have good theoretical grasp of the models but have mainly used them for risk management (thus generating paths and analysing what happens to a portfolio or the balance sheet of an enterprise)