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Abstract
Pricing and risk-managing modern exotic interest rate derivatives requires an interest rate model that has a rich volatility structure, multiple sources of randomness, ability to calibrate to a large/complete set of vanilla options (swaptions and caps), and ability to control volatility smile and rate decorrelation. An intriguing alternative to the above is the class of quadratic Gaussian models. While not widely known -- and even then more familiar to academics than practitioners -- the models have certain attractive properties. They are Markovian in the number of yield curve factors, the state variables are Gaussian and they can generate volatility smiles. As the quadratic model can be fitted quite closely to the market volatility smile, constant maturity swap caps and floors are typically priced by the model near the market. Comparing the model with the SV and LV Cheyette models, as in the previous section, the author's see good agreement for other smile-dependent exotics such as Bermuda swaptions.