Imperial College London

ProfessorDamianoBrigo

Faculty of Natural SciencesDepartment of Mathematics

Chair in Mathematical Finance
 
 
 
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Contact

 

damiano.brigo

 
 
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Location

 

805Weeks BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@inproceedings{Brigo,
author = {Brigo, D and Mai and Jan and Scherer, M and Sloot, H},
publisher = {World Scientific Publishing Co.},
title = {Consistent iterated simulation of multivariate defaults: Markov indicators, lack of memory, extreme-value copulas, and the Marshall–Olkin distribution},
url = {http://hdl.handle.net/10044/1/58307},
}

RIS format (EndNote, RefMan)

TY  - CPAPER
AB - A current market-practice to incorporate multivariate defaults in global riskfactorsimulations is the iteration of (multiplicative) i.i.d. survival indicator incrementsalong a given time-grid, where the indicator distribution is based on acopula ansatz. The underlying assumption is that the behavior of the resultingiterated default distribution is similar to the one-shot distribution. It is shownthat in most cases this assumption is not fulfilled and furthermore numericalanalysis is presented that shows sizeable differences in probabilities assignedto both “survival-of-all” and “mixed default/survival” events. Moreover, theclasses of distributions for which probabilities from the “terminal one-shot”and “terminal iterated” distribution coincide are derived for problems considering“survival-of-all” events as well as “mixed default/survival” events. Forthe former problem, distributions must fulfill a lack-of-memory type property,which is, e.g., fulfilled by min-stable multivariate exponential distributions.These correspond in a copula-framework to exponential margins coupled viaextreme-value copulas. For the latter problem, while looping default inspiredmultivariate Freund distributions and more generally multivariate phase-type distributions could be a solution, under practically relevant and reasonableadditional assumptions on portfolio rebalancing and nested distributions, theunique solution is the Marshall–Olkin class.
AU - Brigo,D
AU - Mai
AU - Jan
AU - Scherer,M
AU - Sloot,H
PB - World Scientific Publishing Co.
TI - Consistent iterated simulation of multivariate defaults: Markov indicators, lack of memory, extreme-value copulas, and the Marshall–Olkin distribution
UR - http://hdl.handle.net/10044/1/58307
ER -