Monte Carlo Simulation - breakthrough in Finance

Warning: Deep material ahead!

The following has been adapted from Reading 9 of the CFA Candidate Body of Knowledge

The latest Finance model to be released in the ever so complex world of Finance is the Monte Carlo. This is a breakthrough finance program that uses a computer to model complex financial instruments in order to gain a valuation whereby analytical methods has no such solution.

Advantages:-

i) Able to model complex financial instruments

Disavantages:-

i) Provides a statistical estimate, rather than a precise solution

So what is this Monte Carlo simulation in a sentence?

Stanford University researcher Sam Savage provided the following "What is the last thing you do before you climb on a ladder? You shake it, and that is Monte Carlo simulation."

For example, currenlty in the Finance world there is no such analytical method to value an Asian-style call option. An Asian-style call option is a right to buy shares of a company whereby the price you pay is the average price of the shares throughout the life of the option and it can only be executed at maturity. Monte Carlo provides a solution to just that.

The specific steps in Monte Carlo are as follows:-

Steps 1-3 describe specifying the simulation.

1. Specify the quantities of interest (option value, for example) in terms of underlying variables. Specify the starting values of the underlying variables.

2. Specify a time grid. Take the horizon in terms of calendar time and split it into a number of subperiods, K.

3. Specify distributional assumptions for the risk factors that drive the underlying variables.

Steps 4-7 describe running the simulation.

4. Using a computer program or spreadsheet function, draw K random values of each risk factor.

5. Calculate the underlying variables using the random observations generated in step 4.

6. Compute the quantities of interest.

7. Go back to Step 4 until a specified number of trials, I, is completed. Finally produce the statistics for the simulation. The key value for our example is the mean value of the total number of simulation trials.

This mean value is the Monte Carlo estimate.

The mean value is the peak of the graph where it has the highest probability

It is awesome because we are finally able to value something that previously we could not value. We can conduct what-if analysis from Monte Carlo, something history automatically does not allow us to do. It works because Monte Carlo randomly generates observations that we can use and apply. And finally after conducting alot of trials, following the Central Limit Theorem, we can say that our mean of the trials is the population parameter (the true value).

It works!