# Copula-GARCH模型下的两资产期权定价

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## Forecasting for DCC Copula GARCH model in R

I'm trying to forecast the Copula Garch Model. I have Copula-GARCH模型下的两资产期权定价 tried to use the dccforecast function with the cGARCHfit but it turns out to be error saying that there is no applicable method for 'dccforecast' applied to an object of class cGARCHfit. So how do actually we forecast the dcc copula garch model?

I have the following reproducible code.

DCC forecasts only work with dccfits. You can try the function cGARCHsim or let go of the Kendall method and go for a dccfit. Though forecasting using cGARCHsim can be a pain if you want to forecast for a longer period ahead.

Details

Since there is no explicit forecasting routine, the user should use this method >for incrementally building up n-ahead forecasts by simulating 1-ahead, >obtaining the means of the returns, sigma, Rho etc and feeding them to the next >round of simulation as starting values. The ‘rmgarch.tests’ folder contains >specific examples which illustrate this particular point.

## 1 模拟数据

B-GARCH(Copula-GARCH模型下的两资产期权定价 1，1)的Copula形式：

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## The Copula GARCH Model

In this vignette, we demonstrate the copula GARCH approach (in general). Note that a special case (with normal or student $$t$$ residuals) is also available 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 in the rmgarch package (thanks Copula-GARCH模型下的两资产期权定价 to Alexios Ghalanos for pointing this out).

## 1 Simulate data

First, we simulate the innovation distribution. Note Copula-GARCH模型下的两资产期权定价 that, for demonstration purposes, we choose a small sample size. Ideally, the sample size should be larger to capture GARCH effects.

Now we simulate two ARMA(1,1)-GARCH(1,1) processes with these Copula-GARCH模型下的两资产期权定价 copula-dependent innovations. To this end, recall that an ARMA( $$Copula-GARCH模型下的两资产期权定价 p_1$$ , $$q_1$$ )-GARCH( $$p_2$$ , $$q_2$$ ) model is given by \begin X_t &= \mu_t + \epsilon_t\ \text\ \epsilon_t = \sigma_t Z_t,\\ \mu_t &= \mu + \sum_^ \phi_k (Copula-GARCH模型下的两资产期权定价 X_-\mu) + \sum_^ \theta_k (X_-\mu_),Copula-GARCH模型下的两资产期权定价 \\ \sigma_t^2 &= \alpha_0 + \sum_^ \alpha_k (X_-\mu_)^2 + \sum_^ \beta_k \sigma_^2. \end

## 2 Fitting procedure based on the simulated 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 data

We now show how to fit an ARMA(1,1)-GARCH(1,1) process to X (we remove the argument fixed.pars from the above specification for estimating these parameters):

Check the (standardized) Z , i.e., the pseudo-observations of the residuals Z :

Fit a $$t$$ copula to the standardized residuals Z . For the marginals, we also assume $$t$$ distributions but with different degrees Copula-GARCH模型下的两资产期权定价 of freedom; for simplicity, the estimation is omitted here.

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Date and time: Fri, 19 Aug 2022 16:47:10 GMT