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A Semi-Explicit Approach to Canary Swaptions in HJM One-Factor Model

  • Marc Henrard

Leveraging the explicit formula for European swaptions and coupon-bond options in the HJM one-factor model, a semi-explicit formula for 2-Bermudan options (also called Canary options) is developed. The European swaption formula is extended to future times. So equipped, one is 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, a semi-explicit formula is provided. Those results lead to a significantly faster and more precise implementation of swaption valuation. The improvements extend even more favourably to sensitivity calculations.

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Article provided by Taylor & Francis Journals in its journal Applied Mathematical Finance.

Volume (Year): 13 (2006)
Issue (Month): 1 ()
Pages: 1-18

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Handle: RePEc:taf:apmtfi:v:13:y:2006:i:1:p:1-18
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  1. Heath, David & Jarrow, Robert & Morton, Andrew, 1992. "Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation," Econometrica, Econometric Society, vol. 60(1), pages 77-105, January.
  2. Marc Henrard, 2004. "Semi-explicit Delta and Gamma for European swaptions in Hull- White one factor model," Finance 0411036, EconWPA, revised 25 Jan 2005.
  3. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-92.
  4. Marc Henrard, 2005. "Bermudan swaptions in Hull-White one-factor model: analytical and numerical approaches," Finance 0505023, EconWPA.
  5. Marc Henrard, 2003. "Explicit bond option and swaption formula in Heath-Jarrow-Morton one factor model," Finance 0310009, EconWPA.
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