IGBM_simulate: Simulate the inhomogeneous geometric Brownian motion (IGBM)...

In LSMRealOptions: Value American and Real Options Through LSM Simulation

Description

The inhomogeneous geometric Brownian motion, also known as the integrated GBM process, is a member of the general affine class of stochastic process that has been reported to be well suited for modelling energy prices. The IGBM_simulate function utilizes antithetic variates as a simple variance reduction technique.

Usage

IGBM_simulate(n, t, reversion_rate, sigma, equilibrium, S0, dt)

Arguments

n	The total number of price paths to simulate
t	The forecasting period, in years
reversion_rate	The reversion rate term of the IGBM process
sigma	The volatility term of the IGBM process
equilibrium	The equilibrium term of the IGBM process
S0	The initial value of the underlying asset
dt	The discrete time step of observations, in years A stochastic process S(t) is an IGBM that follows the following continuous-time stochastic differential equation: dS(t) = reversion_rate(equilibrium - S(t)) dt + sigma dW(t) Where 'reversion_rate' is the rate of reversion term, 'equilibrium' is the equilibrium value the process reverts towards, 'sigma' the volatility term and W(t) is defined as a Weiner process.

Value

A matrix of simulated price paths of the IGBM 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 <- IGBM_simulate(n = 100,
                         t = 1,
                         reversion_rate = 1,
                         sigma = 0.2,
                         equilibrium = 100,
                         S0 = 100,
                         dt = 1/12)

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