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

 `1` ```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

 ```1 2 3 4 5 6 7``` ```## 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.