Simulating a Stochastic Volatility Process
svsim is used to produce realizations of a stochastic volatility (SV)
process.
svsim(len, mu = -10, phi = 0.98, sigma = 0.2, nu = Inf, rho = 0)
len |
length of the simulated time series. |
mu |
level of the latent log-volatility AR(1) process. The defaults
value is |
phi |
persistence of the latent log-volatility AR(1) process. The
default value is |
sigma |
volatility of the latent log-volatility AR(1) process. The
default value is |
nu |
degrees-of-freedom for the conditional innovations distribution.
The default value is |
rho |
correlation between the observation and the increment of the
log-volatility. The default value is |
This function draws an initial log-volatility h_0 from the stationary
distribution of the AR(1) process defined by phi, sigma, and mu.
Then the function jointly simulates the log-volatility series
h_1,...,h_n with the given AR(1) structure, and the “log-return” series
y_1,...,y_n with mean 0 and standard deviation exp(h/2).
Additionally, for each index i, y_i can be set to have a conditionally heavy-tailed
residual (through nu) and/or to be correlated with (h_{i+1}-h_i)
(through rho, the so-called leverage effect, resulting in asymmetric “log-returns”).
The output is a list object of class svsim containing
y |
a vector of length |
vol |
a vector of length
|
vol0 |
The initial volatility |
para |
a named list with five elements |
The function generates the “log-returns” by
y <- exp(-h/2)*rt(h, df=nu). That means that in the case of nu < Inf
the (conditional) volatility is sqrt(nu/(nu-2))*exp(h/2), and that corrected value
is shown in the print, summary and plot methods.
To display the output use print, summary and plot. The
print method simply prints the content of the object in a moderately
formatted manner. The summary method provides some summary statistics
(in %), and the plot method plots the the simulated 'log-returns'
y along with the corresponding volatilities vol.
Gregor Kastner gregor.kastner@wu.ac.at
## Simulate a highly persistent SV process of length 500 sim <- svsim(500, phi = 0.99, sigma = 0.1) print(sim) summary(sim) plot(sim) ## Simulate an SV process with leverage sim <- svsim(200, phi = 0.94, sigma = 0.15, rho = -0.6) print(sim) summary(sim) plot(sim) ## Simulate an SV process with conditionally heavy-tails sim <- svsim(250, phi = 0.91, sigma = 0.05, nu = 5) print(sim) summary(sim) plot(sim)
Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.