Monte Carlo Method (Part II – Financial derivatives)

Before we move on to applying the Monte Carlo Method (or Monte Carlo Simulation) to calculating the value of financial derivatives, we have to understand very well what is a financial derivative, what kind of financial derivatives exist, differences between them and what factors actually influence the value of a financial derivative.

Simply put, derivatives are one of the three financial instruments: stocks (equities and shares)  and debt (for example: mortgages and bonds). A derivative is a contract and like every contract it ensures to the parties some rights and obligations and it has a value. The object of this contract is called an ”underlying” and it can be an asset or an interest rate. So basically, the subjects (parties) of this contract are ”making a bet” over the value of an asset, an index or an interest rate (to be more specific, over the future value of the asset, index or interest rate). They do so from different reasons: to protect themselves from price movements (called hedging) or to speculate from this price movements and earn money.

Monte Carlo Method (part I)

Today, I’m going to explain as simple (and as thoroughly) as possible a method used in a lot of areas for different computations and for obtaining number results based on random samples. I’m not just going to explain it, but also show how to apply this method in Java (if someone wants the Python version, just let me know in the comments section).

So, what’s Monte Carlo Method? Well, according to wikipedia, Monte Carlo method is used mostly in physical and mathematical problems and is very useful when it is difficult or impossible to apply other mathematical methods. Not very clear, is it? In a (very) simplified version, Monte Carlo can be explained like this: a method that uses randomly generated numbers to calculate something. This method is used in mathematics, physics, engineering, finance, AI development etc, but I am more interested in it’s financial applications, financial derivatives and investments evaluation to be more precise. There is no consensus on how Monte Carlo should be defined, so it will be easier just to show you. It is important to know that usually Monte Carlo methods works with pseudo-random numbers as well.