A Python simulation algorithm for the generalised hyperbolic process based on point process simulation methods.
To use the simulator, import the GeneralisedHyperbolic class from the generalisedhyperbolic.py file:
from generalisedhyperbolic import GeneralisedHyperbolic
In order to initialise a GeneralisedHyperbolic object, the 5 arguments characterising the distribution are lam, gamma, delta, beta, sigma. By default the rate is defined as 1, optionally any rate value can be provided. To run the residual approximation method using a Brownian motion with drift, set residual_mode='Gaussian'.
simulator = GeneralisedHyperbolic(lam=lam, gamma=gamma, delta=delta, beta=beta, sigma=sigma, residual_mode='Gaussian')
Jump magnitudes can be generated as
x_series = simulator.simulate_jumps()
where the corresponding jump times are
t_series = np.random.uniform(low=0., high=1., size=x_series.size)
Some example code templates are provided in simulation.ipynb.