Monte Carlo Simulation

What is Monte Carlo Simulation?

Monte Carlo Simulation is a method of valuing options where there are multiple variables that have different outcomes. An example would be if the option was to be valued in Australian Dollars, but is an option for a share that has a US Dollar share price. In this example, the two variables are the share price and the AUD/USD exchange rate.

How Does it Work?

Monte Carlo Simulation is named after the Monte Carlo Casino, as it is a method that takes a number of random samples – like a series of cards being played in a card game – in order to arrive at the value of the option.

 

In the above example, the value of the option would be calculated using various random inputs for share price and exchange rate. The value of the option would then be worked out based on the numerous outcomes, not unlike how counting cards at the casino enables the player to work out the likelihood of the next card being played.

How is this useful for valuing options?

Commonly, options will have exercise or vesting conditions that rely on profit targets or shareholder return targets being met. In order to value options with these conditions, various random samples are taken of the outcomes of the conditions, and the value derived from these samples.

This is particularly useful where there are two or more outcomes that influence the value, as this sampling method delivers a value that could not otherwise be worked out using a direct mathematical formula e.g. Black-Scholes model.

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