Friday, 7 November 2014

Talk : A Defence of the Monte Carlo Simulation

Interesting Cafe Sci talk recently by Dr Nira Chamberlain on the "Monte Carlo" Simulation and how, in Dr Chamberlains view, it had been unfairly blamed for the 2008 financial crisis. This post is based on the talk, with a little extra linkage thrown in.

Dr Chamberlain is a professional mathematician, has been named as one of the UK's 100 leading practical scientists, and is an advocate for mathematics (see also here).

The Monte Carlo simulation is a way of solving mathematical problems by taking multiple random samples rather than trying to "calculate" the answer. For example, rather than trying to calculate the average time to complete a maze, say, a Monte Carlo Simulation would repeatedly try to go through a maze, taking random decisions at each junction, and see how how long it took, on average, to get to the other side.

Perhaps the first use of a Monte Carlo simulation was by French polymath Pierre-Simon Laplace, who used it to estimate the value of pi.

But it was only with the advent of electronic computers, which could quickly perform many thousands of calculations, that Monte Carlo simulations really came into their own, most famously to help the design of the first nuclear bombs in the Manhatten project. It was here that it was given the name "Monte Carlo Method" as it reminded one of the researchers of gambling behaviour in the famous Monte Carlo casino.

After WW2, Monte Carlo simulations were used in applications ranging from engineering to computational biology

An important use of the Monte Carlo simulation is in financial modelling. Dr Chamberlain explained their use, using the "maze" as an analogy for a financial product. Imagine two traders, Trader A and Trader B...

Trader A to Trader B : Here is a maze, and here is £60million pounds on the table. When the clock starts, you begin the maze and I'll start taking away £1million very minute. If you get through the maze in less than an hour, you keep any money left on the table - but if it takes you MORE than an hour, you have to give me £1million for every minute over an hour that it takes you. Do you want to take this bet? (optional evil laugh here)

Trader B (thinks) : The question I need to know the answer to, right now, is how long it takes on average to get through the maze.

And this is where the Monte Carlo simulation comes in. The simulation will have many attempts to get through the maze, and the results are likely for form some kind of frequency distribution like this :

That is all well and good - the problem comes if, in real life the maze is more complicated than the one in the simulation, and the probability distribution is actually like this :

Dr Chamberlain explained that this mismatch between theory and the real world is exactly what happened to financial models in the wake of the 2008 sub-prime defaults, and was a big factor in the resulting financial crisis.

And, worse that this, when the trades lost money the traders thought they had just been unlucky (because their simulation was wrong), so bet again...and again.

Dr Chamberlain commented that JP Morgan had released the Monte Carlo method to the financial marketplace in 1992 [as part of their RiskMetrics methodology] but, in doing so they failed to adequately warn the market about some of the dangers in using the method. The 2008 crisis left many wondering whether Monte Carlo simulations were to blame. Dr Chamberlain gave examples such as an article entitled "Is Financial Monte Carlo Simulation Dead"

However, as suggested in the talks title - Dr Chamberlain was here to defend the Monte Carlo method, and felt that the problem was more to do with poor inputs and assumptions rather than the method itself, commenting that :

i) When the underlying conditions change, so should the assumptions in any relevant Monte Carlo simulations.

ii) A crisis similar had previously occurred in 1998, when LTCM went bust having lost $4.6billion due to the Russian and Far Eastern economic crises distorting the market. [BFTF notes that LTCM was dripping with Economics Nobel Prize winners and that the subsequently bought out company went bust again in 2009].

iii) The market had been warned about the risks of unexpected marked events, for example in the Black Swan theory and in a paper presented at the International Congress of Mathematicians 2002

iv) The Winner Effect, where testosterone fuels increasingly risky trading behaviour.

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