Consistent Iterated Simulation of Multivariate Defaults: Markov Indicators, Lack of Memory, Extreme-Value Copulas, and the Marshall–Olkin Distribution

Damiano Brigo, Jan-Frederik Mai, Matthias Scherer and Henrik Sloot

Chapter 3 in Innovations in Insurance, Risk- and Asset Management:Proceedings of the Innovations in Insurance, Risk- and Asset Management Conference, 2018, pp 47-93 from World Scientific Publishing Co. Pte. Ltd.

Abstract: A current market-practice to incorporate multivariate defaults in global risk-factor simulations is the iteration of (multiplicative) i.i.d. survival indicator increments along a given time-grid, where the indicator distribution is based on a copula ansatz. The underlying assumption is that the behavior of the resulting iterated default distribution is similar to the one-shot distribution. It is shown that in most cases this assumption is not fulfilled and furthermore numerical analysis is presented that shows sizable differences in probabilities assigned to both “survival-of-all” and “mixed default/survival” events. Moreover, the classes 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. For the 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 via extreme-value copulas. For the latter problem, while looping default inspired multivariate Freund distributions and more generally multivariate phase-type distributions could be a solution, under practically relevant and reasonable additional assumptions on portfolio rebalancing and nested distributions, the unique solution is the Marshall–Olkin class.

Keywords: Insurance; Actuarial Science; Risk Measure; Reinsurance; Copula; Replicating Portfolio; Bayesian Finance; Risk Classification; Stochastic Dominance; Dynamic Hedging; Autoregressive Hidden Markov Models; Exchange-Traded Funds; Uncertainty Quantification; Fixed Income; Stochastic Processes for Finance (search for similar items in EconPapers)
JEL-codes: G22 G32 (search for similar items in EconPapers)
Date: 2018
References: Add references at CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.worldscientific.com/doi/pdf/10.1142/9789813272569_0003 (application/pdf)
https://www.worldscientific.com/doi/abs/10.1142/9789813272569_0003 (text/html)
Ebook Access is available upon purchase.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wsi:wschap:9789813272569_0003

Ordering information: This item can be ordered from

Access Statistics for this chapter

More chapters in World Scientific Book Chapters from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().