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Copula-GARCH模型下的两资产期权定价

这里,Copula密度的参数θc包含t分布的自由度以及相关系数矩阵或协方差矩阵自回归方程中的参数,共3个参数,θi和θf则分别包含了两个一元GARCH方程的参数以及t分布的自由度。对这个似然函数来说,同时得到所有参数的极大似然估计较为困难,因此实际中仍然采用两步估计法,第一步利用一元GARCH模型来估计边际分布的参数:
。 内容来自股民网校

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.

Appreciate your kind assistance.

1 Answer 1

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.

R语言中的copula GARCH模型拟合时间序列并模拟分析

在这个文章中,我们演示了copula GARCH方法(一般情况下)。

由Kaizong Ye,Sherry Deng撰写

1 模拟数据

Copula-GARCH类方法

B-GARCH(Copula-GARCH模型下的两资产期权定价 1,1)的Copula形式:
学炒股,上股民网校

其中,为标准残差的边际分布密度函数,是Copula函数。本文中我们采用二元t分布Copula函数,二元t分布Copula密度函数形式如下:

Copula-GARCH类方法

其中Rt是相关系数矩阵,v是t分布自由度,是自由度为v的单变量标准t分布函数的反函数。

Copula-GARCH类方法

对于常相关系数GARCH,相关系数的估计较为简单,可以计算样本序列的Kendall’sτ,根据t-Copula估计的相关系数与Kendall’sτ的一一对应关系:,直接得到固定的相关数。

对于时变相关系数和动态相关系数模型,则仍然使用极大似然估计。模型残差的联合密度函数:,其中是Copula密度函数,则对数似然函数:

Copula-GARCH类方法

这里,Copula密度的参数θc包含t分布的自由度以及相关系数矩阵或协方差矩阵自回归方程中的参数,共3个参数,θi和θf则分别包含了两个一元GARCH方程的参数以及t分布的自由度。对这个似然函数来说,同时得到所有参数的极大似然估计较为困难,因此实际中仍然采用两步估计法,第一步利用一元GARCH模型来估计边际分布的参数:
。 内容来自股民网校

Copula-GARCH类方法

第二步估计Copula密度函数参数:

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.

Copula-GARCH模型下的两资产期权定价

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

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