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A Lévy-Driven Asset Price Model with Bankruptcy and Liquidity Risk

In: From Statistics to Mathematical Finance

Author

Listed:
  • Patrick Bäurer

    (University of Freiburg, Mathematical Institute)

  • Ernst Eberlein

    (University of Freiburg, Mathematical Institute)

Abstract

We present a new asset price model, which is an enhancement of the exponential Lévy model. The possibility of bankruptcy is modelled by a single jump to zero, whereby higher probabilities for this event lead to lower asset prices. We emphasize in particular the dependence between the asset price and the probability of default. Explicit valuation formulas for European options are established by using the Fourier-based valuation method. The formulas can numerically be computed fast and thus allow to calibrate the model to market data. On markets which are not perfectly liquid, the law of one price does no longer hold and the cost of unhedgeable risks has to be taken into account. This aspect is incorporated in the recently developed two price theory (see Cherny and Madan (2010)), which is discussed and applied to the proposed defaultable asset price model.

Suggested Citation

  • Patrick Bäurer & Ernst Eberlein, 2017. "A Lévy-Driven Asset Price Model with Bankruptcy and Liquidity Risk," Springer Books, in: Dietmar Ferger & Wenceslao González Manteiga & Thorsten Schmidt & Jane-Ling Wang (ed.), From Statistics to Mathematical Finance, chapter 0, pages 387-416, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-50986-0_19
    DOI: 10.1007/978-3-319-50986-0_19
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