Consistent Iterated Simulation of Multivariate Defaults: Markov Indicators, Lack of Memory, Extreme-Value Copulas, and the Marshall–Olkin Distribution
| Autor: | Damiano Brigo, Henrik Sloot, Matthias Scherer, Jan-Frederik Mai |
|---|---|
| Přispěvatelé: | Lehrstuhl für Finanzmathematik |
| Rok vydání: | 2018 |
| Předmět: |
Stepwise default simulation
default dependence default simulation extreme-value copulas Marshall-Olkin distribution nested margining Freund distribution looping default models multivariate phase-type distribution Multivariate statistics Markov chain Iterated function Multiplicative function Copula (linguistics) Applied mathematics Extreme value theory ddc Exponential function Ansatz Mathematics |
| Zdroj: | Innovations in Insurance, Risk-and Asset Management |
| DOI: | 10.1142/9789813272569_0003 |
| Popis: | A current market-practice to incorporate multivariate defaults in global riskfactor 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 sizeable 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. |
| Databáze: | OpenAIRE |
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