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Copula-GARCH模型下的两资产期权定价

Copula-based Multivariate GARCH Model with Copula-GARCH模型下的两资产期权定价 Uncorrelated Dependent Errors (2006)

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Copula-GARCH模型下的两资产期权定价
Venue:Journal of Econometrics, Forthcoming
Citations:22 - 2 self

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Abstract

Multivariate GARCH (MGARCH) models are usually estimated under multivariate nor-mality. In this paper, for non-elliptically distributed financial returns, we propose copula-based multivariate GARCH (C-MGARCH) model with uncorrelated dependent errors, which are generated through a linear combination of dependent random variables. The dependence structure is controlled by a copula function. Our new C-MGARCH model nests a conven-tional MGARCH model as a special case. We Copula-GARCH模型下的两资产期权定价 apply this idea to the three MGARCH models, namely, the dynamic conditional correlation (DCC) model of Engle (2002), the varying cor-relation (VC) model of Tse and Tsui (2002), and the BEKK model of Engle and Kroner (1995). Monte Carlo experiment is conducted to illustrate the performance of C-MGARCH vs MGARCH models. Empirical analysis with a pair of the U.S. equity indices and two pairs of the foreign exchange rates indicates that the C-MGARCH models outperform DCC, Copula-GARCH模型下的两资产期权定价 VC, and BEKK in terms of in-sample model selection criteria (likelihood, AIC, SIC) and out-of-sample multivariate density forecast.

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README.md

Method of calculating VaR ( Value at risk) using ARMA-GJR_GARCH and COPULA method

Value at Risk (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 VaR) is one of the most widely used risk measure in risk management. It is defined as the worst loss to be expected of a portfolio over a given time horizon at a given confidence level. We estimate portfolio VaR using an approach combin- ing Copula functions, Extreme Value Theory (EVT) and GARCH models. We apply this approach to a portfolio consisting of stock indices from CTG, MSN, VIC, VNM (Vietnam). To estimate the VaR of this portfolio, we first use an asymmetric GARCH model and an EVT method to model the marginal distributions of each log returns series and then use Copula functions (Gaussian, Student’s t, Clayton, Gumbel and Frank) to link the marginal Copula-GARCH模型下的两资产期权定价 distributions together into a multivariate distribution. We then use Monte Carlo Simulation (MCS) approach to find estimates of the portfolio VaR. To check the goodness of fit of the approach we use Backtesting methods. From the results, we conclude Copula-GARCH模型下的两资产期权定价 that, in general the GARCH-EVT-Copula approach performs well and specifically the GARCH-EVT-Student’s t Copula outperforms all other GARCH-EVT-Copulas and traditional methods such as Historical Simulation (HS) and Variance Covariance (VC).

Keywords: Value at Risk (VaR), Copula, GARCH, Extreme Value Theory (EVT), Backtesting.

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Method of calculating VaR ( Value at risk) using ARMA-GJR_GARCH and COPULA method

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 Copula-GARCH模型下的两资产期权定价 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 Copula-GARCH模型下的两资产期权定价 developed non-ASEAN indexes. The preliminary dynamic equiciorrelation estimates Copula-GARCH模型下的两资产期权定价 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, Copula-GARCH模型下的两资产期权定价 although the ASEAN indexes have higher extreme risk, Copula-GARCH模型下的两资产期权定价 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 a portfolio. As a complementary analysis, we put a 50 percent constraint on Brent in the portfolios, and then the portfolios with the non-ASEAN indexes have better risk-minimizing results.

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