Simulate CIR-type stochastic-volatility innovations

Generates shocks driven by a Cox-Ingersoll-Ross (square-root) stochastic variance process, discretized with the Euler-Maruyama scheme, for use as sim_psy1(..., e = sim_vol_cir(...)).

Usage

sim_vol_cir(
  n,
  kappa = 0.03,
  theta = 0.25,
  xi = 0.1,
  sigma0_sq = theta,
  seed = NULL
)

Arguments

n: Number of innovations to generate.
kappa, theta, xi: Positive CIR parameters (speed of mean reversion, long-run variance and volatility of volatility).
sigma0_sq: Non-negative starting variance. Defaults to theta.
seed: An object specifying if and how the random number generator (rng) should be initialized. It is either NULL or an integer, which is passed to set.seed before the simulation. If you set it, the value is saved as the "seed" attribute of the returned value. The default, NULL, leaves the state of the rng unchanged and returns .Random.seed as the "seed" attribute. Results are reproducible across the parallel and the non-parallel option when you use the same seed.

Value

A numeric vector of length n.

Details

$$d\sigma^2(r) = \kappa(\theta - \sigma^2(r))dr + \xi\sigma(r)dB(r)$$

discretized over n steps of r in $[0, 1]$. The variance is reflected at zero if a step would take it negative. The default parameters ($\kappa=0.03$, $\theta=0.25$, $\xi=0.1$) match the robustness design of Harvey, Leybourne & Zu (2019), which is "representative of Bollerslev and Zhou (2002)".

References

Harvey, D.I., Leybourne, S.J. & Zu, Y. (2019). "Testing explosive bubbles with time-varying volatility." Econometric Reviews, 38(10), 1131-1151.

Examples

sim_vol_cir(199, seed = 1) %>%
  autoplot()