GBM_simulate: Simulate the geometric Brownian motion (GBM) stochastic...

In LSMRealOptions: Value American and Real Options Through LSM Simulation

Description

GBM is a commonly used stochastic process to simulate the price paths of stock prices and other assets, in which the log of the asset follows a random walk process with drift. The GBM_simulate function utilizes antithetic variates as a simple variance reduction technique.

Usage

GBM_simulate(n, t, mu, sigma, S0, dt)

Arguments

n	The total number of price paths to simulate
t	The forecasting period, in years
mu	The drift term of the GBM process
sigma	The volatility term of the GBM process
S0	The initial value of the underlying asset
dt	The discrete time step of observations, in years

Details

A stochastic process S(t) is a geometric brownian motion that follows the following continuous-time stochastic differential equation:

dS(t)/S(t) = mu dt + sigma dW(t)

Where 'mu' is the drift term, 'sigma' the volatility term and W(t) is defined as a Weiner process.

The GBM is log-normally distributed.

Value

A matrix of simulated price paths of the GBM process. Each column corresponds to a simulated price path, and each row corresponds to a simulated observed price of the simulated price paths at each discrete time period.

Examples

## 100 simulations of 1 year of monthly price paths:
Simulated <- GBM_simulate(n = 100,
                         t = 1,
                         mu = 0.05,
                         sigma = 0.2,
                         S0 = 100,
                         dt = 1/12)

LSMRealOptions documentation built on June 26, 2021, 5:06 p.m.