Analytical Pricing of American Bond Options in the Heath-Jarrow-Morton Model
We study the optimal stopping problem of pricing an American Put option on a Zero Coupon Bond (ZCB) in the Musiela's parametrization of the Heath-Jarrow-Morton (HJM) model for forward interest rates. First we show regularity properties of the price function by probabilistic methods. Then we find an infinite dimensional variational formulation of the pricing problem by approximating the original optimal stopping problem by finite dimensional ones, after a suitable smoothing of the payoff. As expected, the first time the price of the American bond option equals the payoff is shown to be optimal.
|Date of creation:||Dec 2012|
|Date of revision:||Mar 2014|
|Publication status:||Published in Stochastic Processes and their Applications 125 (2015) 678-707|
|Contact details of provider:|| Web page: http://arxiv.org/|
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- Björk, Tomas & Landen, Camilla, 2000. "On the construction of finite dimensional realizations for nonlinear forward rate models," SSE/EFI Working Paper Series in Economics and Finance 420, Stockholm School of Economics.
- Michał Barski & Jerzy Zabczyk, 2012. "Forward rate models with linear volatilities," Finance and Stochastics, Springer, vol. 16(3), pages 537-560, July.
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- Tomas Björk & Bent Jesper Christensen, 1999.
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Wiley Blackwell, vol. 9(4), pages 323-348.
- Björk, Tomas & Christensen, Bent Jesper, 1997. "Interest Rate Dynamics and Consistent Forward Rate Curves," SSE/EFI Working Paper Series in Economics and Finance 209, Stockholm School of Economics.
- repec:spr:compst:v:50:y:1999:i:1:p:135-147 is not listed on IDEAS
- Camilla Landén & Tomas Björk, 2002. "On the construction of finite dimensional realizations for nonlinear forward rate models," Finance and Stochastics, Springer, vol. 6(3), pages 303-331.
- Carl Chiarella & Oh Kwon, 2003. "Finite Dimensional Affine Realisations of HJM Models in Terms of Forward Rates and Yields," Review of Derivatives Research, Springer, vol. 6(2), pages 129-155, May.
- 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.
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