Title:	Odhad tržního rizika na bází Lévyho modelů a časový horizont
Other Titles:	Market risk estimation via Lévy models and time horizon
Authors:	Kresta, Aleš Tichý, Tomáš
Citation:	E+M. Ekonomie a Management = Economics and Management. 2012, č. 4, s. 147-158.
Issue Date:	2012
Publisher:	Technická univerzita v Liberci
Document type:	článek article
URI:	http://www.ekonomie-management.cz/download/1379591261_c994/2012_04+Odhad+trzniho+rizika+na+bazi+Levyho+modelu+a+casovy+horizont.pdf http://hdl.handle.net/11025/17479
ISSN:	1212-3609 (Print) 2336-5604 (Online)
Keywords:	míra rizika;Lévyho modely;sponové funkce;portfolio
Keywords in different language:	risk measure;Lévy models;copula functions;portfolio
Abstract in different language:	Modeling, measuring, and managing the risk is an inherent part of risk management in financial institutions. For those institutions, that are active at financial markets, the market risk plays a significant role. The market risk arises from unexpected changes of market prices of equities, interest rates, foreign currencies, and commodities. In this paper we apply a popular example of subordinated Lévy models – the variance gamma model – in order to estimate the risk of internationally diversified portfolio. The variance gamma model is applied in order to estimate the marginal distribution of particular risk factors (stock indices and currencies). Then, two examples of ordinary elliptical copula functions are used in order to create the portfolio, ie. dependent returns for particular assets. We assume Gaussian copula function and Student copula functions. While both copula functions are strictly symmetric, the latter one allows us to stress the tails of the portfolio distribution. For comparison purposes, also standard Brownian motion is assumed. In order to assess the quality of both models, basic descriptive statistics of portfolio returns distribution are evaluated and next, the risk measures Value at Risk and Conditional Value at Risk for several distinct significance levels are provided. The calculation is done for one day and two- weeks horizons. We show, that symmetrical copula functions can decrease the advantage of variance gamma model (it provides skewed distribution for the marginals, which cannot be, however, compensated by symmetric copula functions). Moreover, we show that the scaling of one day VaR into 10-days VaR, might be misleading.
Rights:	© Technická univerzita v Liberci CC BY-NC 4.0
Appears in Collections:	Číslo 4 (2012) Číslo 4 (2012)

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