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About Long-Term Cross-Currency Bermuda Swaption Pricing

Author

Listed:
  • Bünyamin Erkan

    (Banque de France)

  • Jean-Luc Prigent

    (University of Cergy-Pontoise)

Abstract

This paper details first the pricing process of a Bermuda swaption and, in a second step, the pricing of a cross-currency Bermuda swaption from a computational point of view. Our aim is to examine the lengthy process that provides a Bermuda swaption price with special attention to the tests used for assessing the coherence of the price. We only consider long-term derivatives that lead to issues related to missing data and require calibration adjustment. We also deal with the sensitivity of the cross-currency swaption price to the choice of model. The standard model to price this kind of options is a 3-factors hybrid model based on the Libor Market Model that typically combines the domestic market, the foreign market and the foreign exchange market. We study the impact of each one of these stochastic factors on the price of a long-term cross-currency Bermuda swaption. In particular, this study illustrates the relation between the cross-currency product and the volatility of each one of the three markets involved (domestic, foreign and the foreign exchange market).

Suggested Citation

  • Bünyamin Erkan & Jean-Luc Prigent, 2020. "About Long-Term Cross-Currency Bermuda Swaption Pricing," Computational Economics, Springer;Society for Computational Economics, vol. 56(1), pages 239-262, June.
    • Handle: RePEc:kap:compec:v:56:y:2020:i:1:d:10.1007_s10614-019-09899-7
    DOI: 10.1007/s10614-019-09899-7
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    1. Leif Andersen & Mark Broadie, 2004. "Primal-Dual Simulation Algorithm for Pricing Multidimensional American Options," Management Science, INFORMS, vol. 50(9), pages 1222-1234, September.
    2. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," The Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-147.
    3. Marc Henrard, 2003. "Explicit bond option and swaption formula in Heath-Jarrow-Morton one factor model," Finance 0310009, University Library of Munich, Germany.
    4. Ernst Eberlein & Nataliya Koval, 2006. "A cross-currency Levy market model," Quantitative Finance, Taylor & Francis Journals, vol. 6(6), pages 465-480.
    5. Marc Henrard, 2005. "Bermudan swaptions in Hull-White one-factor model: analytical and numerical approaches," Finance 0505023, University Library of Munich, Germany.
    6. Marc Henrard, 2003. "Explicit Bond Option Formula In Heath–Jarrow–Morton One Factor Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 6(01), pages 57-72.
    7. Jensen, Malene Shin & Svenstrup, Mikkel, 2002. "Efficient Control Variates and Strategies for Bermudan Swaptions in a Libor Market Model," Finance Working Papers 02-23, University of Aarhus, Aarhus School of Business, Department of Business Studies.
    8. Denis Belomestny, 2011. "Pricing Bermudan options by nonparametric regression: optimal rates of convergence for lower estimates," Finance and Stochastics, Springer, vol. 15(4), pages 655-683, December.
    9. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
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