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exuber (version 0.2.1)

sim_div: Simulation of dividends

Description

Simulate (log) dividends from a random walk with drift.

Usage

sim_div(n, mu, sigma, r = 0.05, log = FALSE, output = c("pf", "d"))

Arguments

n

A strictly 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

A logical. If true dividends follow a lognormal distribution.

output

A character string giving the fundamental price("pf") or dividend series("d"). Default is `pf'.

Value

A numeric vector of length n.

Details

If log is set to FALSE (default value) the 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 for 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).

References

West, K. D. (1988). Dividend innovations and stock price volatility. Econometrica: Journal of the Econometric Society, p. 37-61.

Examples

Run this code
# NOT RUN {
# Price is the sum of the bubble and fundamental components
# 20 is the scaling factor
pf <- sim_div(100, r = 0.05, output = "pf")
pb <- sim_evans(100, r = 0.05)
p <- pf + 20*pb
# }

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