Lies, damned lies and statistics

It’s mid-summer, holiday time, so why should we be too serious? I thought a few examples of how seemingly logical thought can lead us in to very weird places might be entertaining.

What’s the best way to ensure you are not blown out of the sky by an aeroplane bomber? Well, I guess the most obvious answer to that is not to get on an aeroplane, but let’s for the purposes of the discussion assume that you have to. So the answer is to carry a bomb on board yourself; statistically, the likelihood of two bombs on the same aircraft is vanishingly small. So if you’ve got one, and you don’t detonate it, of course, surely you will be safe?

Aficionados of the TV series Blackadder will no doubt recognise this (paraphrased) exchange, between Captain Blackadder and Private Baldrick:

Blackadder: Baldrick, what’s that you are holding?

Baldrick: It’s a bullet, sir, on which I have written my name.

Blackadder: Why have you done that?

Baldrick: Well, sir, they say that there is somewhere a bullet with your name written on it. So if I keep mine in my pocket, I shall be safe, because nobody will be able to shoot it at me.

Blackadder: Aaahhh……

Statistically, both of those scenarios make logical sense, always assuming in the Baldrick case that you believe the original premise that there is a bullet with your name on it.

Then, of course, we have the kind of opposite approach. Those people, for example, who play the lottery, yet will resist playing today a number which came up in the last draw; but the numbers have no memory, and the probability of drawing any one is the same, regardless of whether it has occurred before or not.

I am fascinated by mathematics and logic - which are in many ways the two sides of the same coin - but I will freely admit that I am a rank amateur. So here’s a final conundrum, which I have pondered over for many years, and which actually has some relevance to the world of metal trading. Does the Black Scholes option pricing model have an intrinsic value of correctness, or does it largely work simply because everyone uses it, and is therefore working off the same page and making it self-fulfilling? Obviously, I happily (and - without giving myself undue flowers - reasonably successfully) used it, mostly in the first decade of this century, but I have always had a lingering doubt that there was no absolute truth in it. Now, both Black and Scholes are far, far cleverer than me, and they are genuine mathematicians, not a linguist who occasionally likes to play with maths, but it seemed to me that the model struggled to handle events which were substantially outside the bell curve. (I don’t think it would be fair to use the collapse of Long Term Capital Management as an arrow to shoot at it - there were many other factors there, as well.)

Option traders, feel free to make your views known.