Monte Carlo simulation is one of the most
famous and widely applied finance techniques. This is a tool that helps us deal with
uncertainty in complex situations.
It steps on the premise that one of
the best ways to deal with multiple uncertain variables is to generate a large
number of random observations for each of them and hence create a joint
distribution regarding the different possible outcomes resulting from the
combination of the random variables.
In layman terms, a Monte Carlo simulation
consists in the following series of steps:
1st – determine the variables that
represent a source of uncertainty
2nd – assume a distribution for each variable
(please note that the distribution that will be chosen is up to the analyst’s discretion);
and of course, the final model predictions will be as good as the analyst’s choice of
distribution for the unknown variables.
Very good.
The 3rd step refers to the following: once we have chosen the different types of
distributions describing the random variables, we need to carry out iterations with
possible realizations for these variables.
And 4th – by repeating the 3rd step many, many
times (hundreds, but more likely thousands of times), we would be able to observe a large
number of possible realization paths that ultimately indicate what could be expected
in terms of the mean of the distribution;
In practice, Monte Carlo simulations
find a large number of applications in the world of finance. Some examples are:
• Options and other derivatives pricing models (when complex features are involved)
• Company valuation (to cross-check results obtained through a
DCF, use Monte Carlo to triangulate results)
• And Risk management (Monte Carlo is
frequently used for Value at Risk estimation and volatility modeling)
The large number of repetitions involved in a Monte Carlo simulation is significantly
facilitated by the strong advents of computing power we have observed in recent years. Running
a Monte Carlo simulation with a very large number of observations does not represent a
significant issue for most models nowadays.
This technique is very useful whenever
an analyst would like to gain an idea of the different possible realizations that could
be obtained through a given distribution function. For example, if a distribution function considers
three possible variables influencing an asset’s price, then by testing for different values of
these variables, we could obtain a good idea about the possible prices of the asset (provided
that the distribution function represents well the development of the asset’s price).
Two main drawbacks should come to mind when performing this technique. First, as already
mentioned the results to be obtained will only be as good as the assumed model according to which
the random output variable is distributed.
And second, this is a statistical approach and not
an analytical one. It doesn’t allow us to examine the impact of some of the separate variables
but instead provides aggregate results.