stochvol (version 3.2.4)

svsim: Simulating a Stochastic Volatility Process

Description

svsim is used to produce realizations of a stochastic volatility (SV) process.

Usage

svsim(len, mu = -10, phi = 0.98, sigma = 0.2, nu = Inf, rho = 0)

Value

The output is a list object of class svsim containing

y

vector of length len containing the simulated data, usually interpreted as ``log-returns''.

vol

vector of length len containing the simulated instantaneous volatilities. These are \(e^{h_t/2}\) if nu == Inf, and they are \(e^{h_t/2} \sqrt{\tau_t}\) for finite nu.

vol0

The initial volatility exp(h_0/2), drawn from the stationary distribution of the latent AR(1) process.

para

a named list with five elements mu, phi, sigma, nu, and rho, containing the corresponding arguments.

latent

vector of the latent state space \(h_t\) for \(t > 0\).

latent0

initial element of the latent state space \(h_0\).

tau

vector of length len containing the simulated auxiliary variables for the Student-t residuals when nu is finite. More precisely, \(\tau_t\sim\text{Gamma}^{-1}(\text{shape}=\nu/2, \text{rate}=\nu/2-1)\).

Arguments

len

length of the simulated time series.

mu

level of the latent log-volatility AR(1) process. The defaults value is -10.

phi

persistence of the latent log-volatility AR(1) process. The default value is 0.98.

sigma

volatility of the latent log-volatility AR(1) process. The default value is 0.2.

nu

degrees-of-freedom for the conditional innovations distribution. The default value is Inf, corresponding to standard normal conditional innovations.

rho

correlation between the observation and the increment of the log-volatility. The default value is 0, corresponding to the basic SV model with symmetric ``log-returns''.

Author

Gregor Kastner

Details

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'').

See Also

svsample

Examples

## 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)