Shock is a product of standard deviation and random shock. This means the stock price is going to drift by the expected return. The first term in the equation is called drift and the second is shock. The generalised form of the Geometric Brownian motion is: Normally, stock prices are believed to follow a Geometric Brownian motion (GMB), which is a Markov process, which means a certain state follows a random walk and its future value is dependent on the current value. This method tries to predict the worst return expected from a portfolio, given a certain confidence interval for a specified time period. It is also possible to model correlated input variables.įor instance, Monte Carlo Simulation can be used to compute the value at risk of a portfolio. It gives an idea of not only what outcome to expect but also the probability of occurrence of that outcome. From probability distribution of input variable, different paths of outcome are generated.Ĭompared to deterministic analysis, the Monte Carlo method provides a superior simulation of risk. Different probability distributions are used for modelling input variables such as normal, lognormal, uniform, and triangular. Monte Carlo Simulation uses probability distribution for modelling a stochastic or a random variable. Along with the outcomes, it can also enable the decision maker see the probabilities of outcomes. Monte Carlo Simulation enables us to see the possible outcomes of a decision, which can thereby help us take better decisions under uncertainty. This can be attributed to the dynamic factors that can impact the outcome of a course of action. Today, it is used extensively for modelling uncertain situations.Īlthough we have a profusion of information at our disposal, it is difficult to predict the future with absolute precision and accuracy. However, given the uncertainty or risk ingrained in a system, it is a useful tool for approximation of realty.ĭescription: The Monte Carlo Simulation technique was introduced during the World War II. It is pertinent to note that Monte Carlo Simulation provides a probabilistic estimate of the uncertainty in a model. The method is used extensively in a wide variety of fields such as physical science, computational biology, statistics, artificial intelligence, and quantitative finance. It is a probabilistic method for modelling risk in a system. Monte Carlo Simulation is the most tenable method used when a model has uncertain parameters or a dynamic complex system needs to be analysed. Different iterations or simulations are run for generating paths and the outcome is arrived at by using suitable numerical computations. The random variables or inputs are modelled on the basis of probability distributions such as normal, log normal, etc. Definition: Monte Carlo Simulation is a mathematical technique that generates random variables for modelling risk or uncertainty of a certain system.