Efficient Control Variates and Strategies for Bermudan Swaptions in a Libor Market Model
AbstractThis paper concerns the problem of valuing Bermudan swaptions in a Libor market model. In particular we consider various eﬃciency improvement techniques for a Monte Carlo based valuation method. We suggest a simplification of the Andersen (2000) exercise strategy and find it to be much more eﬃcient. Furthermore, we test a range of control variates for Bermudan swaptions using a control variate technique for American options proposed in Rasmussen (2002). Application of these eﬃciency improvements in the Primal-Dual simulation algorithm of Andersen & Broadie (2001) improves both upper and lower bounds for the price estimates. For the Primal-Dual simulation algorithm we examine the variance-bias trade-oﬀ between the numbers of outer an inner paths. Finally, we demonstrate that the presence of stochastic volatility increases the expected losses from using the simple strategy in Andersen (2000).
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Bibliographic InfoPaper provided by University of Aarhus, Aarhus School of Business, Department of Business Studies in its series Finance Working Papers with number 02-23.
Length: 35 pages
Date of creation: 09 May 2002
Date of revision:
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Bermudan Swaptions; Control Variates; Exercise Strategy; Primal-Dual Algorithm; Stochastic Volatility;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2003-05-15 (All new papers)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Leif Andersen & Jesper Andreasen, 2000. "Volatility skews and extensions of the Libor market model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 7(1), pages 1-32.
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- Andersen, Torben G. & Lund, Jesper, 1997. "Estimating continuous-time stochastic volatility models of the short-term interest rate," Journal of Econometrics, Elsevier, vol. 77(2), pages 343-377, April.
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- Broadie, Mark & Glasserman, Paul, 1997. "Pricing American-style securities using simulation," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1323-1352, June.
- Longstaff, Francis A. & Santa-Clara, Pedro & Schwartz, Eduardo S., 2001. "Throwing away a billion dollars: the cost of suboptimal exercise strategies in the swaptions market," Journal of Financial Economics, Elsevier, vol. 62(1), pages 39-66, October.
- Farshid Jamshidian, 1997. "LIBOR and swap market models and measures (*)," Finance and Stochastics, Springer, vol. 1(4), pages 293-330.
- Pierre Collin-Dufresne & Robert S. Goldstein, 2002. "Do Bonds Span the Fixed Income Markets? Theory and Evidence for Unspanned Stochastic Volatility," Journal of Finance, American Finance Association, vol. 57(4), pages 1685-1730, 08.
- Rasmussen, Nicki Søndergaard, 2002. "Efficient Control Variates for Monte-Carlo Valuation of American Options," Finance Working Papers 02-17, University of Aarhus, Aarhus School of Business, Department of Business Studies.
- Svenstrup, Mikkel, 2003. "On the Suboptimality of Single-Factor Exercise Strategies for Bermudan Swaptions," Finance Working Papers 02-24, University of Aarhus, Aarhus School of Business, Department of Business Studies.
- Svenstrup, Mikkel, 2005. "On the suboptimality of single-factor exercise strategies for Bermudan swaptions," Journal of Financial Economics, Elsevier, vol. 78(3), pages 651-684, December.
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