Abstract.
We present an iterative procedure for computing the optimal Bermudan stopping time, hence the Bermudan Snell envelope. The method produces an increasing sequence of approximations of the Snell envelope from below, which coincide with the Snell envelope after finitely many steps. Then, by duality, the method induces a convergent sequence of upper bounds as well. In a Markovian setting the presented procedure allows to calculate approximative solutions with only a few nestings of conditional expectations and is therefore tailor-made for a plain Monte Carlo implementation. The method may be considered generic for all discrete optimal stopping problems. The power of the procedure is demonstrated for Bermudan swaptions in a full factor LIBOR market model.
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Mathematics Subject Classification:
62L15, 65C05, 91B28
JEL Classification:
G13
Supported by the DFG Research Center "MATHEON" (FZT 86) in Berlin.The present paper strongly benefited from Christian Bender who gave many suggestions which have led to a substantially improved presentation, and showed the termination of the iterative procedure from Lemma [4.5]. We thank the anonymous referees for their useful remarks and pointing out the termination issue as well. J.S. is grateful to Martin Schweizer for helpful discussions and suggestions. This work is supported by the DFG Research Center MATHEON in Berlin.
Manuscript received: June 2004; final version received: August 2005
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Kolodko, A., Schoenmakers, J. Iterative construction of the optimal Bermudan stopping time. Finance Stochast. 10, 27–49 (2006). https://doi.org/10.1007/s00780-005-0168-5
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DOI: https://doi.org/10.1007/s00780-005-0168-5