132 Frequently Asked Questions In Quantitative Finance
What is Monte Carlo Simulation?
Short Answer
Monte Carlo simulations are a way of solving probabil-
istic problems by numerically ‘imagining’ many possible
scenarios or games so as to calculate statistical proper-
ties such as expectations, variances or probabilities of
certain outcomes. In finance we use such simulations to
represent the future behaviour of equities, exchange
rates, interest rates, etc. so as to either study the
possible future performance of a portfolio or to price
derivatives.
Example
We hold a complex portfolio of investments, we would
like to know the probability of losing money over the
next year since our bonus depends on us making a
profit. We can estimate this probability by simulating
how the individual components in our portfolio might
evolve over the next year. This requires us to have a
model for the random behaviour of each of the assets,
including the relationship or correlation between them,
if any.
Some problems which are completely deterministic can
also be solved numerically by running simulations, most
famously finding a value forπ.
Long Answer
It is clear enough that probabilistic problems can be
solved by simulations. What is the probability of tossing
heads with a coin, just toss the coin often enough and
you will find the answer. More on this and its relevance
to finance shortly. But many deterministic problems
can also be solved this way, provided you can find a
probabilistic equivalent of the deterministic problem.
A famous example of this is Buffon’s needle, a problem
