simdiff: Simulation of diffusion processes

In Techtonique/ESGtoolkit: Toolkit for Monte Carlo Simulations

Simulation of diffusion processes

Description

Simulates various diffusion processes including Geometric Brownian Motion (GBM), Cox-Ingersoll-Ross (CIR), and Ornstein-Uhlenbeck (OU) processes.

Usage

simdiff(
  n,
  horizon,
  frequency = c("annual", "semi-annual", "quarterly", "monthly", "weekly", "daily"),
  model = c("GBM", "CIR", "OU"),
  x0,
  theta1 = NULL,
  theta2 = NULL,
  theta3 = NULL,
  lambda = NULL,
  mu_z = NULL,
  sigma_z = NULL,
  p = NULL,
  eta_up = NULL,
  eta_down = NULL,
  eps = NULL,
  start = NULL,
  seed = 123
)

Arguments

n	Number of simulations/scenarios
horizon	Time horizon for simulation
frequency	Frequency of observations: "annual", "semi-annual", "quarterly", "monthly", "weekly", or "daily"
model	Type of diffusion process: "GBM", "CIR", or "OU"
x0	Initial value
theta1	First parameter (drift for GBM, mean reversion for CIR/OU)
theta2	Second parameter (volatility for GBM, long-term mean for CIR/OU)
theta3	Third parameter (optional, used for some models)
lambda	Jump intensity parameter (optional)
mu_z	Mean of jump size (optional)
sigma_z	Standard deviation of jump size (optional)
p	Probability parameter (optional)
eta_up	Upward jump size (optional)
eta_down	Downward jump size (optional)
eps	Pre-generated random shocks (optional)
start	Starting time (optional)
seed	Random seed for reproducibility

Details

The function simulates various diffusion processes with different frequencies. For GBM, theta1 represents the drift and theta2 the volatility. For CIR and OU processes, theta1 is the mean reversion speed and theta2 is the long-term mean.

Value

A time series object containing the simulated paths

Examples

# Simulate GBM process
eps <- simshocks(n = 10, horizon = 5, frequency = "quarterly")
sim_GBM <- simdiff(n = 10, horizon = 5, frequency = "quarterly",
                   model = "GBM", x0 = 100, theta1 = 0.03, theta2 = 0.1,
                   eps = eps)

# Simulate CIR process
sim_CIR <- simdiff(n = 10, horizon = 5, frequency = "quarterly",
                   model = "CIR", x0 = 0.04, theta1 = 1.5, theta2 = 0.04,
                   theta3 = 0.2, eps = eps)

Techtonique/ESGtoolkit documentation built on June 11, 2025, 6:24 p.m.