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A fractional credit model with long range dependent default rate

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  • Biagini, Francesca
  • Fink, Holger
  • Klüppelberg, Claudia

Abstract

Motivated by empirical evidence of long range dependence in macroeconomic variables like interest rates we propose a fractional Brownian motion driven model to describe the dynamics of the short and the default rate in a bond market. Aiming at results analogous to those for affine models we start with a bivariate fractional Vasicek model for short and default rate, which allows for fairly explicit calculations. We calculate the prices of corresponding defaultable zero-coupon bonds by invoking Wick calculus. Applying a Girsanov theorem we derive today’s prices of European calls and compare our results to the classical Brownian model.

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  • Biagini, Francesca & Fink, Holger & Klüppelberg, Claudia, 2013. "A fractional credit model with long range dependent default rate," Stochastic Processes and their Applications, Elsevier, vol. 123(4), pages 1319-1347.
    • Handle: RePEc:eee:spapps:v:123:y:2013:i:4:p:1319-1347
    DOI: 10.1016/j.spa.2012.12.006
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    1. Duncan, T.E., 2006. "Prediction for some processes related to a fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 76(2), pages 128-134, January.
    2. Robert J. Elliott & John Van Der Hoek, 2003. "A General Fractional White Noise Theory And Applications To Finance," Mathematical Finance, Wiley Blackwell, vol. 13(2), pages 301-330, April.
    3. Vladas Pipiras & Murad S. Taqqu, 2002. "Deconvolution of fractional brownian motion," Journal of Time Series Analysis, Wiley Blackwell, vol. 23(4), pages 487-501, July.
    4. Jost, Céline, 2006. "Transformation formulas for fractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 116(10), pages 1341-1357, October.
    5. Andrew Carverhill, 1994. "When Is The Short Rate Markovian?," Mathematical Finance, Wiley Blackwell, vol. 4(4), pages 305-312, October.
    6. David K. Backus & Stanley E. Zin, 1993. "Long-memory inflation uncertainty: evidence from the term structure of interest rates," Proceedings, Federal Reserve Bank of Cleveland, pages 681-708.
    7. Duncan, Tyrone E. & Fink, Holger, 2011. "Corrigendum to "Prediction for some processes related to a fractional Brownian motion"," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1336-1337, August.
    8. Paolo Guasoni & Miklós Rásonyi & Walter Schachermayer, 2010. "The fundamental theorem of asset pricing for continuous processes under small transaction costs," Annals of Finance, Springer, vol. 6(2), pages 157-191, March.
    9. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305, World Scientific Publishing Co. Pte. Ltd..
    10. Paolo Guasoni & Mikl'os R'asonyi & Walter Schachermayer, 2008. "Consistent price systems and face-lifting pricing under transaction costs," Papers 0803.4416, arXiv.org.
    11. Alberto Ohashi, 2008. "Fractional term structure models: No-arbitrage and consistency," Papers 0802.1288, arXiv.org, revised Sep 2009.
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