Simulate (log) dividends from a random walk with drift.
Usage
sim_div(
n,
mu,
sigma,
r = 0.05,
log = FALSE,
output = c("pf", "d"),
seed = NULL
)Arguments
- n
A positive integer specifying the length of the simulated output series.
- mu
A scalar indicating the drift.
- sigma
A positive scalar indicating the standard deviation of the innovations.
- r
A positive value indicating the discount factor.
- log
Logical. If true dividends follow a lognormal distribution.
- output
A character string giving the fundamental price("pf") or dividend series("d"). Default is
pf.- seed
An object specifying if and how the random number generator (rng) should be initialized. Either NULL or an integer will be used in a call to
set.seedbefore simulation. If set, the value is saved as "seed" attribute of the returned value. The default, NULL, will not change rng state, and return .Random.seed as the "seed" attribute. Results are reproducible across the parallel and non-parallel option when the same seed is used.
Details
If log is set to FALSE (default value) dividends follow:
$$d_t = \mu + d_{t-1} + \epsilon_t$$
where \(\epsilon \sim \mathcal{N}(0, \sigma^2)\). The default parameters are \(\mu = 0.0373\), \(\sigma^2 = 0.1574\) and \(d[0] = 1.3\) (the initial value of the dividend sequence). The above equation can be solved to yield the fundamental price:
$$F_t = \mu(1+r)r^{-2} + r^{-1}d_t$$
If log is set to TRUE then dividends follow a lognormal distribution or log(dividends) follow:
$$\ln(d_t) = \mu + \ln(d_{t-1}) + \epsilon_t$$
where \(\epsilon \sim \mathcal{N}(0, \sigma^2)\). Default parameters are \(\mu = 0.013\), \(\sigma^2 = 0.16\). The fundamental price in this case is:
$$F_t = \frac{1+g}{r-g}d_t$$
where \(1+g=\exp(\mu+\sigma^2/2)\). All default parameter values are those suggested by West (1988).
