ajd.sim.wh

The goal of ajd.sim.wh is to simulate exactly the Heston Stochastic Volatility (SV) model and its Affine Jump Diffusion (AJD) extensions using the Wu-Hu algorithm (Wu-Hu, 2024), hence the name ajd.sim.wh. The extended models include

• SVJ: SV model with jumps in the price process.

• SVCJ: SV model with contemporaneous jumps both in the price and variance processes.

References:

• Kyriakou, I., Brignone, R., & Fusai, G. (2024). Unified moment-based modeling of integrated stochastic processes. Operations Research, 72(4), 1630-1653.

Installation

You can install the development version of ajd.sim.wh like so:

# library(devtools)
install_github("xmlongan/ajd.sim.wh")

Example

This is a basic example which shows you how to simulate some return (not the price) samples of the Heston SV model and plot a histogram of these simulated returns:

library(ajd.sim.wh)
# Heston SV
v0 = 0.010201; k = 6.21; theta = 0.019; sigma = 0.61; rho = -0.7
r = 0.0319; tau = 1

par_hest = list(v0=v0, k=k, theta=theta, sigma=sigma, rho=rho, h=tau)
moms = rep(0, 8)
for (i in 2:8) {moms[i] = eval_mom_hest(ajd.sim.wh::fmu.hest[[i]], par_hest)}

N = 1000 # number of samples
Y = ajd.sim.wh::rpearson(1000, moms)

beta = (1  -exp(-k * tau)) / (2 * k)
Ymean = (r - theta/2) * tau - beta * (v0 - theta)

Y = Y + Ymean
hist(Y, main="Heston SV model")

If you want to simulate samples from the other two SV models, use:

• price_svj() for the SVJ model,

• price_svcj() for the SVCJ model.

Pricing the European call option Using Monte Carlo simulation

If your are interested in pricing the European call option using Monte Carlo simulation for the Heston SV, SVJ and SVCJ models. Please refer to functions ?price_hest, ?price_svj and ?price_svcj.