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Copula-GARCH模型下的两资产期权定价

Copula-GARCH模型下的两资产期权定价

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Copula-GARCH模型下的两资产期权定价

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Abstract

This paper minimizes the risk of Brent oil in a multivariate portfolio, with three risk-minimizing goals: variance, parametric value-at-risk (VaR), and semiparametric value-at-risk. Brent oil is combined with five emerging ASEAN (Association of Southeast Asian Nations) stock indexes and five more developed non-ASEAN indexes. The preliminary dynamic equiciorrelation estimates indicate that the ASEAN stock indexes are less integrated and thus potentially better for diversification purposes. The portfolio results show that the ASEAN indexes are better hedges for oil in terms of minimum variance and minimum VaR. However, although the ASEAN indexes have higher extreme risk, we find that a portfolio with these indexes has slightly lower modified VaR than a portfolio with the non-ASEAN indexes. The reason is probably the higher variance and higher equicorrelation of the non-ASEAN indexes, because these inputs affect the value of the modified downside risk of Copula-GARCH模型下的两资产期权定价 a portfolio. As a complementary analysis, we put a 50 percent constraint on Brent Copula-GARCH模型下的两资产期权定价 in the portfolios, and then the portfolios Copula-GARCH模型下的两资产期权定价 with the non-ASEAN indexes have better risk-minimizing results.

Value-At-Risk (VaR) curve with Copula-GARCH model (R)

I'm trying to creave a VaR curve with the Copula-GARCH model in R. Here's what I have:

Getting stock Copula-GARCH模型下的两资产期权定价 prices for Boeing & Airbus and calculating Copula-GARCH模型下的两资产期权定价 yields:

Creating an optimal portfolio:

2D distribution of yields:

The problem is about obtaining a VaR curve (here's splitting the sample into a test and examinating sample):

How can I combine GARCH and copulas for fitting the model and creating a VaR curve?

Copula-Garch Model

Ciprian Necula Senior Lecturer, DOFIN, Faculty of Finance and Banking, Bucharest University of Economics, Bucharest, Romania Romania; Researcher, Center for Advanced Research in Finance and Banking (CARFIB),Bucharest University of Economics, Bucharest; Researcher,Centrul de Analiză şi Prognoză Economico-Financiară (CAPEF) [email protected]

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  • https://doi.org/10.1080/1331677X.2010.11517408

Original scientific paper

A Copula-Garch Modelcopula-Garch Model

In the present study we develop a new two-dimensional Copula-GARCH model. This type of two-dimensional process is characterized by a dependency structure modeled using a copula function. For the marginal densities we employ a GARCH(1,1) model with innovations drawn from a t-Student distribution. The model can be easily extended by using more sophisticated processes for the marginal densities. The static specification of the model assumes that the dependency structure of the two data series does not vary in time implying that the Copula-GARCH模型下的两资产期权定价 parameters of the copula function are constant. On the other hand, the dynamic specification models explicitly the dynamics of these parameters. We econometrically estimate the parameters of the two specifications using various copula functions, focusing on the mixture between the Gumbel and Clayton copulas. We employ daily index returns from two emerging and two developed financial markets. The main finding is that including a varying dependency structure improves the goodness-of-fit of the Copula-GARCH model. 1

U ovom smo istraživanju Copula-GARCH模型下的两资产期权定价 razvili novi dvodimenzionalni Copula-GARCH model. Ovu vrstu dvodimenzionalnih procesa karakterizira zavisna struktura stvorena koristeći spojnu funkciju (kopulu). Za marginalne gustoće koristili smo GARCH(1,1) model s inovacijama preuzetim iz t-Student distribucije. Model se može lako proširiti koristeći sofisticiranije procese za marginalne gustoće. Statička specifikacija modela pretpostavlja da zavisna struktura dva niza podataka ne varira u vremenu te tako podrazumijeva da su parametri spojne funkcije konstantni. S druge strane, dinamička specifikacija eksplicitno određuje dinamiku ovih parametara. Ekonometrijski procjenjujemoparametre dvije specifikacije koristeći razne spojne funkcije, uz naglasak na mješavinu između Gumbelove i Claytonove kopule. Koristili smo dnevne indekse zarade s dva razvijena i dva financijska tržišta u razvoju. Glavni nalaz upućuje na to da uključivanje promjenjive zavisne strukture poboljšava sukladnost distribucije Copula-GARCH modela.