Monte Carlo Method (Part III – Option pricing)

Now that we are familiar with both the Monte Carlo Simulation and option concept, we can move on to determining a way to apply Monte Carlo in option pricing. The are a numerous option pricing models, each with specific assumptions that apply to specific option types, but the most famous is the Black-Scholes model and we will cover this model at a later date in order to compare the results of Monte Carlo Simulation to the results obtained by applying Black-Scholes model (which is believed to be one of the most exact option pricing model).

We’re going to apply the Monte Carlo simulation to calculate the value of an European call option (an options that gives the right to buy shares only at a specific date in the future!), because Black-Scholes can be applied only to European options (one of its limits) and we have to be able to compare the results and see the error rate.

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.