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Value‐at‐risk Trade‐off and Capital Allocation with Copulas
Author(s) -
Cherubini Umberto,
Luciano Elisa
Publication year - 2001
Publication title -
economic notes
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.274
H-Index - 19
eISSN - 1468-0300
pISSN - 0391-5026
DOI - 10.1111/j.0391-5026.2001.00055.x
Subject(s) - copula (linguistics) , econometrics , joint probability distribution , marginal distribution , economics , extreme value theory , normality , capital allocation line , stock (firearms) , tail dependence , marginal value , mathematics , statistics , microeconomics , multivariate statistics , profit (economics) , random variable , mechanical engineering , engineering
This paper uses copula functions to evaluate tail probabilities and market risk trade‐offs at a given confidence level, dropping the joint normality assumption on returns. Copulas enable one to represent distribution functions separating the marginal distributions from the association structure. We present an application to two stock market indices: for each market we recover the marginal probability distribution. We then calibrate copula functions and recover the joint distribution. The estimated copulas directly give the joint probabilities of extreme losses. Their level curves measure the trade‐off between losses over different desks. This trade‐off can be exploited for capital allocation and is shown to depend on fat tails. (J.E.L.: C14, G19, G29).