IGBM_simulate {LSMRealOptions}

Simulate the inhomogeneous geometric Brownian motion (IGBM) stochastic process through Monte Carlo 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)