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The Journal of Derivatives

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Article

Vulnerable Exotic Derivatives

Marcos Escobar, Mirco Mahlstedt, Sven Panz and Rudi Zagst
The Journal of Derivatives Spring 2017, 24 (3) 84-102; DOI: https://doi.org/10.3905/jod.2017.24.3.084
Marcos Escobar
is a professor in the Department of Statistical and Actuarial Sciences at Western University in London, ON, Canada.
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  • For correspondence: marcos.escobar@uwo.ca
Mirco Mahlstedt
is a researcher at the Chair of Mathematical Finance, Technische Universität München, in Munich, Germany.
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  • For correspondence: mirco.mahlstedt@tum.de
Sven Panz
is a researcher at the Chair of e-Finance, Goethe Universität Frankfurt, in Frankfurt, Germany.
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  • For correspondence: panz@wiwi.uni-frankfurt.de
Rudi Zagst
is a professor at the Chair of Mathematical Finance, Technische Universität München, in Munich, Germany.
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  • For correspondence: zagst@tum.de
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Abstract

Understanding and managing counterparty credit risk exposure in derivatives contracts has become a crucial element of real-world trading as well as theoretical modeling. But existing models are limited in the number of securities involved and in the assumed dynamics of the underlying asset returns processes. In this article, the authors present a framework with two counterparties who enter into a derivatives contract in which either of them may default, and the derivative’s payoff depends on the joint distribution of n different assets. Three specific examples illustrate application of the approach: an option on a security in which both counterparties are subject to default risk; a vulnerable spread option, in which one risky counterparty issues an option tied to the price spread between two other assets; and a defaultable swap with one underlying and two risky counterparties who commit to a series of future cash flows. The resulting pricing formulas are mathematically complicated, but as closed-form solutions (with the caveat that integral expressions are approximated using finite step size and number of terms in an infinite series), they are much more efficient than Monte Carlo simulation in reaching a given level of accuracy.

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The Journal of Derivatives: 24 (3)
The Journal of Derivatives
Vol. 24, Issue 3
Spring 2017
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Vulnerable Exotic Derivatives
Marcos Escobar, Mirco Mahlstedt, Sven Panz, Rudi Zagst
The Journal of Derivatives Feb 2017, 24 (3) 84-102; DOI: 10.3905/jod.2017.24.3.084

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Vulnerable Exotic Derivatives
Marcos Escobar, Mirco Mahlstedt, Sven Panz, Rudi Zagst
The Journal of Derivatives Feb 2017, 24 (3) 84-102; DOI: 10.3905/jod.2017.24.3.084
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  • Article
    • Abstract
    • NOTATION AND FINANCIAL SETTING
    • MATHEMATICAL RESULTS
    • PRICING OF VULNERABLE EXOTIC PRODUCTS
    • EMPIRICAL ANALYSIS
    • VULNERABLE RAINBOW BARRIER OPTION
    • VULNERABLE SPREAD OPTION
    • BILATERAL DEFAULTABLE SWAP
    • CONCLUSION
    • APPENDIX
    • ENDNOTES
    • REFERENCES
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