Abstract
We propose a new default contagion model, where default may originate from the performance of a specific firm itself but can also be directly influenced by defaults of other firms. The default intensities of our model depend on smoothly varying macroeconomic variables, driven by a long-range dependent process. In particular, we focus on the pricing of defaultable derivatives whose defaults depend on the macroeconomic process and may be affected by the contagion effect. In our approach we are able to provide explicit formulas for prices of defaultable derivatives at any time t∈[0,T]. Finally we calculate some examples explicitly, where the macroeconomic factor process is given by a functional of the fractional Brownian motion with Hurst index \(H >\frac{1}{2}\).
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Acknowledgements
We thank Damir Filipović for interesting discussions and remarks. We gratefully acknowledge the numerical support of Vincenzo Ferrazzano, who calculated the prices for the different scenarios of Example 4.10. Finally, we thank Holger Fink und Peter Hepperger for careful reading of the paper, whose comments improved the paper considerably.
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Biagini, F., Fuschini, S., Klüppelberg, C. (2011). Credit Contagion in a Long Range Dependent Macroeconomic Factor Model. In: Di Nunno, G., Øksendal, B. (eds) Advanced Mathematical Methods for Finance. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18412-3_4
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DOI: https://doi.org/10.1007/978-3-642-18412-3_4
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