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A Lévy-driven asset price model with bankruptcy and liquidity risk. (English) Zbl 1383.62232
Ferger, Dietmar (ed.) et al., From statistics to mathematical finance. Festschrift in honour of Winfried Stute. Cham: Springer (ISBN 978-3-319-50985-3/hbk; 978-3-319-50986-0/ebook). 387-416 (2017).
Summary: 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 [D. B. Madan and A. Cherny, Int. J. Theor. Appl. Finance 13, No. 8, 1149–1177 (2010; Zbl 1208.91148)]), which is discussed and applied to the proposed defaultable asset price model.
For the entire collection see [Zbl 1383.62010].
MSC:
62P05 Applications of statistics to actuarial sciences and financial mathematics
60G51 Processes with independent increments; Lévy processes
60H30 Applications of stochastic analysis (to PDEs, etc.)
91B25 Asset pricing models (MSC2010)
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