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Azéma martingales for Bessel and CIR processes and the pricing of Parisian zero‐coupon bonds

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  • Angelos Dassios
  • Jia Wei Lim
  • Yan Qu

Abstract

In this paper, we study the excursions of Bessel and Cox–Ingersoll–Ross (CIR) processes with dimensions 0

Suggested Citation

  • Angelos Dassios & Jia Wei Lim & Yan Qu, 2020. "Azéma martingales for Bessel and CIR processes and the pricing of Parisian zero‐coupon bonds," Mathematical Finance, Wiley Blackwell, vol. 30(4), pages 1497-1526, October.
    • Handle: RePEc:bla:mathfi:v:30:y:2020:i:4:p:1497-1526
    DOI: 10.1111/mafi.12248
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    References listed on IDEAS

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    1. Freddy Delsaen, 1993. "Consols In the Cir Model," Mathematical Finance, Wiley Blackwell, vol. 3(2), pages 125-134, April.
    2. Chen, Ren-Raw & Scott, Louis O, 1992. "Pricing Interest Rate Options in a Two-Factor Cox-Ingersoll-Ross Model of the Term Structure," The Review of Financial Studies, Society for Financial Studies, vol. 5(4), pages 613-636.
    3. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    4. Robert A. Jarrow & David Lando & Fan Yu, 2008. "Default Risk And Diversification: Theory And Empirical Implications," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 19, pages 455-480, World Scientific Publishing Co. Pte. Ltd..
    5. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    6. Damiano Brigo & Aurélien Alfonsi, 2005. "Credit default swap calibration and derivatives pricing with the SSRD stochastic intensity model," Finance and Stochastics, Springer, vol. 9(1), pages 29-42, January.
    7. Peter Carr & Vadim Linetsky, 2006. "A jump to default extended CEV model: an application of Bessel processes," Finance and Stochastics, Springer, vol. 10(3), pages 303-330, September.
    8. Dassios, Angelos & Lim, Jia Wei, 2013. "Parisian option pricing: a recursive solution for the density of the Parisian stopping time," LSE Research Online Documents on Economics 58985, London School of Economics and Political Science, LSE Library.
    9. Angelos Dassios & Shanle Wu, 2010. "Perturbed Brownian motion and its application to Parisian option pricing," Finance and Stochastics, Springer, vol. 14(3), pages 473-494, September.
    10. Dassios, Angelos & Lim, Jia Wei, 2017. "An efficient algorithm for simulating the drawdown stopping time and the running maximum of a Brownian motion," LSE Research Online Documents on Economics 68823, London School of Economics and Political Science, LSE Library.
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    Cited by:

    1. Gongqiu Zhang & Lingfei Li, 2021. "A General Approach for Parisian Stopping Times under Markov Processes," Papers 2107.06605, arXiv.org.

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