Bob Browning's blog

I went to see The Power of Yes yesterday.  It is a very good explanation of the financial crisis as explained by a playwright – David Hare.  I recommend it – the two hours flew by.  However there was one small item I worried about.  There was a comment about ‘Monte-Carlo methods’ being used by AIG which  got a cheap laugh which I thought unfair.  Monte Carlo methods are not about gambling – they are about minimising risk.

To explain (please bear with me I will get to the point):

The formula used to price a lot of the securities that caused the problem is the Black-Scholes formula – which one of the actors wrote up on a board.  But the statement was made that it ‘predicts’ the future.  Which is doesn’t; unless a statement like ‘if you flip a coin if will be heads 50% of the time’ can be said to be predicting the future.  The Black-Scholes formula just says that if you assume that security prices vary at random then the price in x days time will be within certain limits y and z, except in very exceptional circumstances.

There are two assumptions built into this which are questionable.

1. Stock prices are random, that is a price will go up or down within limits independent of the history of the price to date.  This is the same as saying that if a coin has come down heads ten times in a row, the odds on it coming down heads again is still 50%.
2. The distribution of price changes is the standard bell-shaped normal distribution.

Number 1 is true enough in day to day trading which is why the formula works.  However if a price has gone down ten days in a row people get scared and start selling so the price continues to crash.

Number 2 is accurate enough for day to day purposes as well except of course when their is a crash.

The other thing that came out was a statement in the AIG accounts that options had been priced using Monte-Carlo methods.  This caused some hilarity but this is unfair.  Monte-Carlo simulation is a long-established and very respectable method.  In fact we used it to model oilfield operations in the 60’s.   What it means is that you run a sequence of pretend trades letting the prices vary according to the rules you set.   If you do this often enough you get a pattern of prices looking forward from which you can deduce the range of prices you can expect.

If you plug in the assumption that the price changes are normally distributed independent and random  then if you run enough simulations you will end up with the same answer as Black-Scholes.   The downside is that you need a computer to run all the simulations rather than a hand-held calculator.  The big upside however is that you are not limited to the  random/normal assumption built into Black-Scholes.  You can model any behaviour you want – including crashes in price.

So Monte-Carlo simulation is potentially a much more powerful and robust method of predicting future price distributions and therefore risk.

Why is it not used more?

• Maybe because it needs so much computer power and time
• Maybe because it is something of a ‘brute strength and ignorance’ approach.  There is no mathematical subtlety with Monte-Carlo.

Whatever it is it deserves more of a centre stage position that it has.