. . . "[B1B5DCFB78E9]" . . "27510" . "2"^^ . . . "portfolio; copula functions; L\u00E9vy models; risk measure"@en . "Modelov\u00E1n\u00ED, m\u011B\u0159en\u00ED a \u0159\u00EDzen\u00ED rizika je d\u016Fle\u017Eitou \u010Dinnost\u00ED v\u0161ech finan\u010Dn\u00EDch instituc\u00ED. Pro ty instituce, kter\u00E9 jsou aktivn\u00ED na finan\u010Dn\u00EDch trz\u00EDch, je d\u016Fle\u017Eit\u00E9 sledovat tr\u017En\u00ED riziko. Tr\u017En\u00ED riziko vznik\u00E1 z d\u016Fvodu mo\u017Enosti vzniku neo\u010Dek\u00E1van\u00FDch zm\u011Bn tr\u017En\u00EDch cen akci\u00ED, \u00FArokov\u00FDch sazeb, m\u011Bnov\u00FDch kurz\u016F a komodit. V tomto \u010Dl\u00E1nku je pou\u017Eit popul\u00E1rn\u00ED pod\u0159\u00EDzen\u00FD L\u00E9vyho model, konkr\u00E9tn\u011B variance-gama model, pro odhad rizika mezin\u00E1rodn\u011B diverzifikovan\u00E9ho portfolia. Variance-gama model je pou\u017Eit pro odhad margin\u00E1ln\u00EDch rozd\u011Blen\u00ED jednotliv\u00FDch rizikov\u00FDch faktor\u016F (ceny akciov\u00FDch index\u016F a m\u011Bnov\u00E9 kurzy). Pro modelov\u00E1n\u00ED z\u00E1vislost\u00ED jsou pou\u017Eity dv\u011B eliptick\u00E9 kopula funkce, konkr\u00E9tn\u011B je uva\u017Eov\u00E1na Gaussova a Studentova kopula funkce. Ob\u011B uva\u017Eovan\u00E9 kopula funkce jsou symetrick\u00E9, ov\u0161em Studentova kopula funkce umo\u017E\u0148uje zohlednit t\u011B\u017Ek\u00E9 konce pravd\u011Bpodobnostn\u00EDho rozd\u011Blen\u00ED. Pro srovn\u00E1vac\u00ED \u00FA\u010Dely je uva\u017Eov\u00E1n rovn\u011B\u017E standardn\u00ED geometrick\u00FD Brown\u016Fv pohyb. Pro ohodnocen\u00ED kvality model\u016F jsou srovn\u00E1v\u00E1ny z\u00E1kladn\u00ED popisn\u00E9 statistiky modelovan\u00FDch pravd\u011Bpodobnostn\u00EDch rozd\u011Blen\u00ED a rovn\u011B\u017E m\u00EDry Value at Risk a conditional Value at Risk pro r\u016Fzn\u00E9 hladiny spolehlivosti. V\u00FDpo\u010Dty jsou provedeny jak pro interval jednoho dne, tak pro dva t\u00FDdny. Bylo zji\u0161t\u011Bno, \u017Ee pou\u017Eit\u00ED symetrick\u00FDch kopula funkc\u00ED vede ke sn\u00ED\u017Een\u00ED v\u00FDhody variance-gama modelu, kter\u00FD umo\u017E\u0148uje modelovat ze\u0161ikmen\u00E9 rozd\u011Blen\u00ED margin\u00E1ln\u00EDch pravd\u011Bpodobnost\u00ED, co\u017E ov\u0161em nem\u016F\u017Ee b\u00FDt kompenzov\u00E1no symetrickou kopula funkc\u00ED. Rovn\u011B\u017E bylo uk\u00E1z\u00E1no, \u017Ee pou\u017E\u00EDvan\u00FD p\u0159epo\u010Det jednodenn\u00ED hodnoty Value at Risk na desetidenn\u00ED nen\u00ED p\u0159esn\u00FD." . "2"^^ . "4" . . . "Odhad tr\u017En\u00EDho rizika na b\u00E1z\u00ED L\u00E9vyho model\u016F a \u010Dasov\u00FD horizont"@cs . . "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 L\u00E9vy models \u2013 the variance gamma model \u2013 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 twoweeks 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."@en . . . "Tich\u00FD, Tom\u00E1\u0161" . . . "CZ - \u010Cesk\u00E1 republika" . "Market risk estimation via L\u00E9vy models and time horizon"@en . . "Odhad tr\u017En\u00EDho rizika na b\u00E1z\u00ED L\u00E9vyho model\u016F a \u010Dasov\u00FD horizont" . . . "Modelov\u00E1n\u00ED, m\u011B\u0159en\u00ED a \u0159\u00EDzen\u00ED rizika je d\u016Fle\u017Eitou \u010Dinnost\u00ED v\u0161ech finan\u010Dn\u00EDch instituc\u00ED. Pro ty instituce, kter\u00E9 jsou aktivn\u00ED na finan\u010Dn\u00EDch trz\u00EDch, je d\u016Fle\u017Eit\u00E9 sledovat tr\u017En\u00ED riziko. Tr\u017En\u00ED riziko vznik\u00E1 z d\u016Fvodu mo\u017Enosti vzniku neo\u010Dek\u00E1van\u00FDch zm\u011Bn tr\u017En\u00EDch cen akci\u00ED, \u00FArokov\u00FDch sazeb, m\u011Bnov\u00FDch kurz\u016F a komodit. V tomto \u010Dl\u00E1nku je pou\u017Eit popul\u00E1rn\u00ED pod\u0159\u00EDzen\u00FD L\u00E9vyho model, konkr\u00E9tn\u011B variance-gama model, pro odhad rizika mezin\u00E1rodn\u011B diverzifikovan\u00E9ho portfolia. Variance-gama model je pou\u017Eit pro odhad margin\u00E1ln\u00EDch rozd\u011Blen\u00ED jednotliv\u00FDch rizikov\u00FDch faktor\u016F (ceny akciov\u00FDch index\u016F a m\u011Bnov\u00E9 kurzy). Pro modelov\u00E1n\u00ED z\u00E1vislost\u00ED jsou pou\u017Eity dv\u011B eliptick\u00E9 kopula funkce, konkr\u00E9tn\u011B je uva\u017Eov\u00E1na Gaussova a Studentova kopula funkce. Ob\u011B uva\u017Eovan\u00E9 kopula funkce jsou symetrick\u00E9, ov\u0161em Studentova kopula funkce umo\u017E\u0148uje zohlednit t\u011B\u017Ek\u00E9 konce pravd\u011Bpodobnostn\u00EDho rozd\u011Blen\u00ED. Pro srovn\u00E1vac\u00ED \u00FA\u010Dely je uva\u017Eov\u00E1n rovn\u011B\u017E standardn\u00ED geometrick\u00FD Brown\u016Fv pohyb. Pro ohodnocen\u00ED kvality model\u016F jsou srovn\u00E1v\u00E1ny z\u00E1kladn\u00ED popisn\u00E9 statistiky modelovan\u00FDch pravd\u011Bpodobnostn\u00EDch rozd\u011Blen\u00ED a rovn\u011B\u017E m\u00EDry Value at Risk a conditional Value at Risk pro r\u016Fzn\u00E9 hladiny spolehlivosti. V\u00FDpo\u010Dty jsou provedeny jak pro interval jednoho dne, tak pro dva t\u00FDdny. Bylo zji\u0161t\u011Bno, \u017Ee pou\u017Eit\u00ED symetrick\u00FDch kopula funkc\u00ED vede ke sn\u00ED\u017Een\u00ED v\u00FDhody variance-gama modelu, kter\u00FD umo\u017E\u0148uje modelovat ze\u0161ikmen\u00E9 rozd\u011Blen\u00ED margin\u00E1ln\u00EDch pravd\u011Bpodobnost\u00ED, co\u017E ov\u0161em nem\u016F\u017Ee b\u00FDt kompenzov\u00E1no symetrickou kopula funkc\u00ED. Rovn\u011B\u017E bylo uk\u00E1z\u00E1no, \u017Ee pou\u017E\u00EDvan\u00FD p\u0159epo\u010Det jednodenn\u00ED hodnoty Value at Risk na desetidenn\u00ED nen\u00ED p\u0159esn\u00FD."@cs . "12"^^ . "E+M Ekonomie a Management" . "1212-3609" . "RIV/61989100:27510/12:86082954!RIV13-GA0-27510___" . "000313469200012" . "RIV/61989100:27510/12:86082954" . "Market risk estimation via L\u00E9vy models and time horizon"@en . . "Odhad tr\u017En\u00EDho rizika na b\u00E1z\u00ED L\u00E9vyho model\u016F a \u010Dasov\u00FD horizont"@cs . . "155855" . . "P(EE2.3.30.0016), P(GA402/08/1237), S" . . "Kresta, Ale\u0161" . "Odhad tr\u017En\u00EDho rizika na b\u00E1z\u00ED L\u00E9vyho model\u016F a \u010Dasov\u00FD horizont" . "15" .