A semi-analytical approach to Canary swaptions in HJM one-factor model

Leveraging the explicit formula for European swaptions and coupon-bond options in HJM one-factor model, we develop a semi-explicit formula for 2-Bermudan options (also called Canary options). We first extend the European swaption formula to future times. We are able to reduce the valuation of a 2-Bermudan swaption to a single numerical integration at the first expiry date. In that integration the most complex part of the valuation of the embedded European swaptions has been simplified in such a way that it has to be performed only once and not for every point.