A Semi-Explicit Approach to Canary Swaptions in HJM One-Factor Model
Economics Working Paper Archive No. 0310008
14 Pages Posted: 31 Dec 2004
Date Written: December 25, 2004
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. So equipped, 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 embedded European swaptions valuation has been simplified to perform it only once and not for every point. In a special but very common in practice case, we also provide a semi-explicit formula. Those results lead to a significantly more precise implementation of swaption valuation. The improvements extend even more favorable to sensitivity calculations.
Keywords: Bermudan option, swaption, bond option, HJM model, Hull-White model, one-factor model, explicit formula, numerical integration
JEL Classification: G13, E43
Suggested Citation: Suggested Citation