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Path dependent options on yields in the affine term structure model

Author

Listed:
  • 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.

Suggested Citation

  • Olivier Scaillet & Boris Leblanc, 1998. "Path dependent options on yields in the affine term structure model," Finance and Stochastics, Springer, vol. 2(4), pages 349-367.
    • 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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    Citations

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    Cited by:

    1. Alexander Lipton, 2020. "Old Problems, Classical Methods, New Solutions," Papers 2003.06903, arXiv.org.
    2. Adrian Prayoga & Nicolas Privault, 2017. "Pricing CIR Yield Options by Conditional Moment Matching," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 24(1), pages 19-38, March.
    3. Bossaerts, P. & Ghysels, E. & Gourieroux, C., 1996. "Arbitrage-Based Pricing when Volatility is Stochastic," Cahiers de recherche 9615, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    4. Paul Lescot, 2009. "On affine interest rate models," Papers 0911.2757, arXiv.org, revised Oct 2011.
    5. Ditlevsen, Susanne, 2007. "A result on the first-passage time of an Ornstein-Uhlenbeck process," Statistics & Probability Letters, Elsevier, vol. 77(18), pages 1744-1749, December.
    6. Curato, Imma Valentina & Mancino, Maria Elvira & Recchioni, Maria Cristina, 2018. "Spot volatility estimation using the Laplace transform," Econometrics and Statistics, Elsevier, vol. 6(C), pages 22-43.
    7. Alexander Novikov & R. E. Melchers & E. Shinjikashvili & N. Kordzakhia, 2003. "First Passage Time of Filtered Poisson Process with Exponential Shape Function," Research Paper Series 109, Quantitative Finance Research Centre, University of Technology, Sydney.
    8. 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, vol. 34(9), pages 2132-2145, September.
    9. Alexander Lipton & Vadim Kaushansky, 2018. "On the First Hitting Time Density of an Ornstein-Uhlenbeck Process," Papers 1810.02390, arXiv.org, revised Oct 2018.
    10. Lingfei Li & Vadim Linetsky, 2015. "Discretely monitored first passage problems and barrier options: an eigenfunction expansion approach," Finance and Stochastics, Springer, vol. 19(4), pages 941-977, October.
    11. Caio Almeida & Jos� Vicente, 2012. "Term structure movements implicit in Asian option prices," Quantitative Finance, Taylor & Francis Journals, vol. 12(1), pages 119-134, February.
    12. Xing, Xiaoyu & Xing, Yongsheng & Yang, Xuewei, 2012. "A note on transition density for the reflected Ornstein–Uhlenbeck process," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 586-591.
    13. Chuang Yi, 2010. "On the first passage time distribution of an Ornstein-Uhlenbeck process," Quantitative Finance, Taylor & Francis Journals, vol. 10(9), pages 957-960.
    14. Dassios, Angelos & Nagaradjasarma, Jayalaxshmi, 2011. "Pricing of Asian options on interest rates in the CIR model," LSE Research Online Documents on Economics 32084, London School of Economics and Political Science, LSE Library.
    15. Patie, Pierre, 2005. "On a martingale associated to generalized Ornstein-Uhlenbeck processes and an application to finance," Stochastic Processes and their Applications, Elsevier, vol. 115(4), pages 593-607, April.

    More about this item

    Keywords

    Term structure; path dependent options; affine model; hitting time; Laplace transform;
    All these keywords.

    JEL classification:

    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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