Efficient Control Variates and Strategies for Bermudan Swaptions in a Libor Market Model
This 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).
|Date of creation:||09 May 2002|
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- Farshid Jamshidian, 1997. "LIBOR and swap market models and measures (*)," Finance and Stochastics, Springer, vol. 1(4), pages 293-330.
- Mark Joshi & Jochen Theis, 2002. "Bounding Bermudan swaptions in a swap-rate market model," Quantitative Finance, Taylor & Francis Journals, vol. 2(5), pages 370-377.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- Miltersen, K. & K. Sandmann & D. Sondermann, 1994.
"Closed Form Solutions for Term Structure Derivatives with Log-Normal Interest Rates,"
Discussion Paper Serie B
308, University of Bonn, Germany.
- Miltersen, Kristian R & Sandmann, Klaus & Sondermann, Dieter, 1997. " Closed Form Solutions for Term Structure Derivatives with Log-Normal Interest Rates," Journal of Finance, American Finance Association, vol. 52(1), pages 409-30, March.
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