###### Probability Distribution of Discrete a ...

Probability Distribution The probability distribution of a random variable \(X\) is basically a... **Read More**

Monte Carlo simulations involve the creation of a computer-based model into which the variabilities and interrelationships between random variables are entered. A spread of results is obtained when the model is run many times – hundreds or thousands of times. Therefore, the method is very useful when the number of random variables is extremely high, making the analysis using ordinary methods very complex.

In finance, we use Monte Carlo simulations to define potential risk. For example, a mutual fund manager may use the method to manage assets and liabilities in a bid to try and establish any downward risk – the risk that liabilities will outgrow the assets, leading to a loss.

The method can also be used in project appraisal. In this regard, a project manager uses the Monte Carlo simulation to establish the financial viability of a project. In most cases, there is an initial cash outlay followed by subsequent costs during a project’s productive life. The project also generates profit at specified times during its lifetime. If the present value of profit outweighs that of costs, the project is considered financially feasible.

However, both profits and costs are likely to be affected by numerous underlying variables, which may include interest rate movements, exchange rate fluctuations, technological changes, labor supply costs, among others. Monte Carlo simulation can incorporate all the variables into a model that can be iterated to highlight all the possible future outcomes of the project. The outcomes are then summarized in terms of probabilities. The least likely outcome and the most likely one can then be deduced.

- Create a model of the project and establish all the interdependencies as well as serial correlations between the variables.
- Specify the probability for the distribution of each key variable present in the model.
- Using random values extracted randomly from the distribution of the variables, simulate the cash flows repeatedly. Hundreds or thousands of simulations are usually performed.
- Record and order all the outputs and establish their probability distributions.

From the results, we can determine the mean profit, the variance as well as skewness of the distribution. Nowadays, financial modeling software, specifically designed to carry out such simulations, can be purchased.

- It is used to value projects that require significant amounts of funds and may have future financial implications on a company.
- It can be used to simulate profits or losses in the online trading of stocks.
- Simulation of the values of assets and liabilities of a pension benefit scheme.
- It can also be used to value complex securities such as American or European options.

- It only provides us with statistical estimates of results, not exact figures.
- It is fairly complex and can only be carried out using specially designed software that may be expensive.
- The complexity of the process may cause errors leading to wrong results that can be potentially misleading.