Bermudan swaptions in Hull-White one-factor model: analytical and numerical approaches
A popular way to value (Bermudan) swaption in a Hull-White or extended Vasicek model is to use a tree approach. In this note we show that a more direct approach through iterated numerical integration is also possible. A brute force numerical integration would lead to a complexity exponential in the number of exercise dates in the base of the number of points ($p^N$). By carefully choosing the integration points and their order we can reduce it to a complexity $pN^2$ versus a quadratic $(pN)^2$ in the tree. We also provide a semi-explicit formula that leads to a faster converging implementation.
|Date of creation:||30 May 2005|
|Date of revision:|
|Note:||Type of Document - pdf; pages: 9. Draft version, comments welcome. Math Subject Classification MSC2000: 91B28, 91B24, 91B70|
|Contact details of provider:|| Web page: http://econwpa.repec.org|
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- Marc Henrard, 2003. "Explicit bond option and swaption formula in Heath-Jarrow-Morton one factor model," Finance 0310009, EconWPA.
- Heath, David & Jarrow, Robert & Morton, Andrew, 1992.
"Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation,"
Econometric Society, vol. 60(1), pages 77-105, January.
- David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305 World Scientific Publishing Co. Pte. Ltd..
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