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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 tried to use the dccforecast function with the cGARCHfit but it turns out to be error saying that there is Copula-GARCH模型下的两资产期权定价 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 Copula-GARCH模型下的两资产期权定价 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 Copula-GARCH模型下的两资产期权定价 returns, sigma, Rho etc and feeding them to the next Copula-GARCH模型下的两资产期权定价 >round of simulation as starting Copula-GARCH模型下的两资产期权定价 values. The ‘rmgarch.tests’ folder contains >specific examples which illustrate 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 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(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 in the rmgarch package (thanks to Alexios Ghalanos for pointing this out).

1 Simulate data

First, Copula-GARCH模型下的两资产期权定价 we simulate the innovation distribution. Note 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-dependent innovations. To this end, recall that an ARMA( \(p_1\) , \(q_1\) )-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 Copula-GARCH模型下的两资产期权定价 &= \mu + \sum_^ \phi_k (X_-\mu) + \sum_^ \theta_k (X_-\mu_),\\ \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 data

We now show how to fit an ARMA(1,1)Copula-GARCH模型下的两资产期权定价 -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 of freedom; for simplicity, the Copula-GARCH模型下的两资产期权定价 estimation is omitted here.

Copula-GARCH模型下的两资产期权定价

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Date and Copula-GARCH模型下的两资产期权定价 time: Fri, 19 Aug 2022 16:47:10 GMT

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