The SystemicRisk package fits (dynamic) CoVaR and MES Regression Models
in the sense that it semiparametrically models the Value at Risk (VaR),
i.e., the
You can install the development version of SystemicRisk from GitHub with:
# install.packages("devtools")
devtools::install_github("TimoDimi/SystemicRisk")This is a basic example which shows you how to solve a common problem:
library(quantmod)
#> Loading required package: xts
#> Loading required package: zoo
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#> Attaching package: 'zoo'
#> The following objects are masked from 'package:base':
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#> as.Date, as.Date.numeric
#> Loading required package: TTR
#> Registered S3 method overwritten by 'quantmod':
#> method from
#> as.zoo.data.frame zoo
library(tidyr)
library(dplyr)
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#> ######################### Warning from 'xts' package ##########################
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#> # work, which breaks lag(my_xts). Calls to lag(my_xts) that you type or #
#> # source() into this session won't work correctly. #
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#> # Use stats::lag() to make sure you're not using dplyr::lag(), or you can add #
#> # conflictRules('dplyr', exclude = 'lag') to your .Rprofile to stop #
#> # dplyr from breaking base R's lag() function. #
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#> Attaching package: 'dplyr'
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#> first, last
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#> filter, lag
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#> intersect, setdiff, setequal, union
library(tsibble)
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#> Attaching package: 'tsibble'
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#> index
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#> intersect, setdiff, union
library(SystemicRisk)
# Get data from Yahoo Finance
data_Symbols <- lapply(c("JPM", "^GSPC"), function(x) {
getSymbols(x,
from = "2000/01/01",
to = "2021/12/31",
periodicity = "daily",
auto.assign = FALSE) %>%
data.frame(Date=zoo::index(.), check.names=FALSE) %>%
rename_all(~stringr::str_replace_all(., paste0(x,"."), ""))
})
names(data_Symbols) <- c("JPM", "SP500")
# Collect data as a tsibble with x and y as column names
data_Assets <- dplyr::bind_rows(data_Symbols, .id = "Asset") %>%
dplyr::group_by(Asset) %>%
dplyr::mutate(Date=lubridate::as_date(Date),
NegReturn= -100*(log(Close) - log(lag(Close)))) %>%
dplyr::select(Date, Asset, NegReturn) %>%
stats::na.omit() %>%
tidyr::pivot_wider(names_from=Asset, values_from=NegReturn) %>%
dplyr::rename(x=JPM, y=SP500) %>%
tsibble::as_tsibble(index=Date)
# Fit a CoCAViaR-SAV-fullA model
CoCAViaR_obj <- SRM(data=data_Assets,
model="CoCAViaR_SAV_fullA",
risk_measure="CoVaR",
beta=0.95,
alpha=0.95)
# Get standard errors and print its summary
summary(CoCAViaR_obj)
#>
#> VaR Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 0.054091 0.160081 0.3379 0.735455
#> lag |X| 0.168976 0.052671 3.2081 0.001344 **
#> lag |Y| 0.178439 0.124771 1.4301 0.152734
#> lag VaR 0.853420 0.059332 14.3837 < 2.2e-16 ***
#>
#> CoVaR Parameter Estimates:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 0.25853 0.58157 0.4445 0.6567
#> lag |X| 0.11912 0.17040 0.6991 0.4845
#> lag |Y| 0.39401 0.30868 1.2764 0.2019
#> lag CoVaR 0.79223 0.19874 3.9863 6.798e-05 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# Plot the time series and estimated (in-sample) VaR/CoVaR
p <- plot(CoCAViaR_obj)
#> Warning: Removed 2 rows containing missing values (`geom_line()`).
## Download VIX index:
data_VIX <- getSymbols("^VIX",
from = "2000/01/01",
to = "2021/12/31",
periodicity = "daily",
auto.assign = FALSE) %>%
data.frame(Date=zoo::index(.), check.names=FALSE) %>%
select(Date, VIX.Close) %>%
rename(VIX = VIX.Close)
#> Warning: ^VIX contains missing values. Some functions will not work if objects
#> contain missing values in the middle of the series. Consider using na.omit(),
#> na.approx(), na.fill(), etc to remove or replace them.
# Merge data frames
data_Assets_VIX <- full_join(data_Assets, data_VIX, by="Date") %>%
mutate(Intercept = 1) %>%
select(Date, x, y, VIX, Intercept) %>%
na.omit()
# Fit a linear MES regression model (with the lagged absolute values of X_t as explanatory variables)
MES_reg <- SRM(data=data_Assets_VIX,
model="joint_linear",
risk_measure="MES",
beta=0.95)
# Get standard errors and print its summary
summary(MES_reg)
#>
#> VaR Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> VIX 0.209109 0.011799 17.7223 < 2.2e-16 ***
#> Intercept -1.092828 0.178286 -6.1296 9.417e-10 ***
#>
#> MES Parameter Estimates:
#> Estimate Std. Error t value Pr(>|t|)
#> VIX 0.124891 0.018235 6.8488 8.255e-12 ***
#> Intercept -0.662195 0.318142 -2.0814 0.03744 *
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# Plot the time series and estimated (in-sample) VaR/MES
p2 <- plot(MES_reg)
#> Warning: Removed 2 rows containing missing values (`geom_line()`).