对两支股票数据,用GARCH模型和二元Copula函数进行拟合之后,如何计算VaR和ES值,给出r代码
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计算VaR和ES值通常需要进行模拟,以下是基于GARCH模型和二元Copula函数的VaR和ES计算的R代码示例:
```r
library(rugarch)
library(copula)
# 假设我们有两支股票的收益率数据为ret1和ret2
# 定义GARCH模型
spec1 <- ugarchspec(variance.model = list(model = "sGARCH", garchOrder = c(1,1)),
mean.model = list(armaOrder = c(1,0), include.mean = TRUE),
distribution.model = "norm")
spec2 <- ugarchspec(variance.model = list(model = "sGARCH", garchOrder = c(1,1)),
mean.model = list(armaOrder = c(1,0), include.mean = TRUE),
distribution.model = "norm")
# 拟合GARCH模型
fit1 <- ugarchfit(spec1, data = ret1)
fit2 <- ugarchfit(spec2, data = ret2)
# 定义二元Copula函数
copula <- normalCopula(param = 0.5, dim = 2)
# 拟合Copula模型
fit.copula <- fitCopula(copula, cbind(fitted(fit1), fitted(fit2)))
# 模拟收益率路径
n.sim <- 10000
sim.ret1 <- rnorm(n.sim, mean = 0, sd = sqrt(fitted(fit1)[nrow(ret1)]))
sim.ret2 <- rnorm(n.sim, mean = 0, sd = sqrt(fitted(fit2)[nrow(ret2)]))
sim.copula <- rCopula(n = n.sim, copula = copula, dispstr = "un", df = Inf)
sim.ret <- qnorm(sim.copula) # 转换为正态分布
sim.ret[,1] <- sim.ret[,1] * sqrt(fitted(fit1)[nrow(ret1)]) + sim.ret1 # 转换为原来的收益率
sim.ret[,2] <- sim.ret[,2] * sqrt(fitted(fit2)[nrow(ret2)]) + sim.ret2
# 计算VaR和ES
alpha <- 0.05
VaR <- quantile(sim.ret, alpha)
ES <- mean(sim.ret[sim.ret <= VaR])
# 输出结果
cat("VaR:", VaR, "\n")
cat("ES:", ES, "\n")
```
需要注意的是,上述代码仅供参考,实际应用中需要根据具体数据进行调整。
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