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Path dependent options on yields in the affine term structure model

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Author Info

  • Olivier Scaillet

    (Institut d'Administration et de Gestion and Département des Sciences Economiques, Université Catholique de Louvain, 3 place Montesquieu, B-1348 Louvain-la-Neuve, Belgique Manuscript)

  • Boris Leblanc

    (Banque Nationale de Paris, Université Paris VII and CREST Laboratoire de Finance Assurance, Bâtiment Malakoff 2 - Timbre J320, 15 Boulevard Gabriel Péri, F-92245 Malakoff Cedex, France)

Abstract

We give analytical pricing formulae for path dependent options on yields in the framework of the affine term structure model. More precisely, European call options such as the arithmetic average call, the call on maximum and the lookback call are examined. For the two last options approximate formulae using the law of hitting times of an Ornstein-Uhlenbeck process are proposed. Numerical implementation is also briefly discussed and results are given in the case of the arithmetic average option.

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Bibliographic Info

Article provided by Springer in its journal Finance and Stochastics.

Volume (Year): 2 (1998)
Issue (Month): 4 ()
Pages: 349-367

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Handle: RePEc:spr:finsto:v:2:y:1998:i:4:p:349-367

Note: received: September 1996; final version received: October 1997
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Related research

Keywords: Term structure; path dependent options; affine model; hitting time; Laplace transform;

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Cited by:
  1. Jang, Bong-Gyu & Yoon, Ji Hee, 2010. "Analytic valuation formulas for range notes and an affine term structure model with jump risks," Journal of Banking & Finance, Elsevier, Elsevier, vol. 34(9), pages 2132-2145, September.
  2. Xing, Xiaoyu & Xing, Yongsheng & Yang, Xuewei, 2012. "A note on transition density for the reflected Ornstein–Uhlenbeck process," Statistics & Probability Letters, Elsevier, Elsevier, vol. 82(3), pages 586-591.
  3. Bossaerts, P. & Ghysels, E. & Gourieroux, C., 1996. "Arbitrage-Based Pricing when Volatility is Stochastic," Cahiers de recherche, Universite de Montreal, Departement de sciences economiques 9615, Universite de Montreal, Departement de sciences economiques.
  4. Alexander Novikov & R. E. Melchers & E. Shinjikashvili & N. Kordzakhia, 2003. "First Passage Time of Filtered Poisson Process with Exponential Shape Function," Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney 109, Quantitative Finance Research Centre, University of Technology, Sydney.
  5. Angelos Dassios & Jayalaxshmi Nagaradjasarma, 2011. "Pricing of Asian options on interest rates in the CIR model," LSE Research Online Documents on Economics, London School of Economics and Political Science, LSE Library 32084, London School of Economics and Political Science, LSE Library.
  6. Ditlevsen, Susanne, 2007. "A result on the first-passage time of an Ornstein-Uhlenbeck process," Statistics & Probability Letters, Elsevier, Elsevier, vol. 77(18), pages 1744-1749, December.

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