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Credit risk modeling using time-changed Brownian motion

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  • T. R. Hurd

Abstract

Motivated by the interplay between structural and reduced form credit models, we propose to model the firm value process as a time-changed Brownian motion that may include jumps and stochastic volatility effects, and to study the first passage problem for such processes. We are lead to consider modifying the standard first passage problem for stochastic processes to capitalize on this time change structure and find that the distribution functions of such "first passage times of the second kind" are efficiently computable in a wide range of useful examples. Thus this new notion of first passage can be used to define the time of default in generalized structural credit models. Formulas for defaultable bonds and credit default swaps are given that are both efficiently computable and lead to realistic spread curves. Finally, we show that by treating joint firm value processes as dependent time changes of independent Brownian motions, one can obtain multifirm credit models with rich and plausible dynamics and enjoying the possibility of efficient valuation of portfolio credit derivatives.

Suggested Citation

  • T. R. Hurd, 2009. "Credit risk modeling using time-changed Brownian motion," Papers 0904.2376, arXiv.org.
  • Handle: RePEc:arx:papers:0904.2376
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    File URL: http://arxiv.org/pdf/0904.2376
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    References listed on IDEAS

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    1. Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241.
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    Cited by:

    1. Marcos Escobar & Peter Hieber & Matthias Scherer, 2014. "Efficiently pricing double barrier derivatives in stochastic volatility models," Review of Derivatives Research, Springer, vol. 17(2), pages 191-216, July.
    2. Hieber, Peter & Scherer, Matthias, 2012. "A note on first-passage times of continuously time-changed Brownian motion," Statistics & Probability Letters, Elsevier, vol. 82(1), pages 165-172.
    3. Thomas R. Hurd & Zhuowei Zhou, 2011. "Two-factor capital structure models for equity and credit," Papers 1110.5846, arXiv.org.
    4. Fernández Lexuri & Hieber Peter & Scherer Matthias, 2013. "Double-barrier first-passage times of jump-diffusion processes," Monte Carlo Methods and Applications, De Gruyter, vol. 19(2), pages 107-141, July.
    5. Cantia, Catalin & Tunaru, Radu, 2017. "A factor model for joint default probabilities. Pricing of CDS, index swaps and index tranches," Insurance: Mathematics and Economics, Elsevier, vol. 72(C), pages 21-35.
    6. Flavia Barsotti, 2012. "Optimal Capital Structure with Endogenous Default and Volatility Risk," Working Papers - Mathematical Economics 2012-02, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.

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