Risk Latte - Black-Scholes in English

Black-Scholes in English

Team latte
Sep 05, 2005

One of the greatest quants that I have come across was one of my ex-colleagues (whom for the want of a better name I shall call "Boss") who taught me a lot about options trading. Boss had no formal background in mathematics and was terribly uncomfortable with equations and formulas. His basic dictum was that if it cannot be explained in plain English then it is not worth doing it. And yet I think he had better grasp of options trading than many of his peers who were such heavy duty quantitative traders. This was early nineties and a revolution was taking place in the field of financial derivatives. Mathematicians and Physicists were making inroads in the field of finance and every day some research paper or the other was coming out with new models of exotic option pricing. In such a world he was almost one of its kind.

In an interview, he once asked a trainee to explain Black-Scholes call pricing equation in one sentence without using any technical terms. The trainee, who would later become his protégé, was himself quite a perceptive guy (despite his age) and started by saying: "Black-Scholes tells us that a call's value is comprised of both the intrinsic value and the time value and that if nothing happens in the market, then the intrinsic value of the stock will decay with time at an exponential rate."

Boss was impressed but perhaps not quite. He knew instinctively that he had found a match who could carry his torch further. But not yet. He actually asked the trainee to do better and simply this even more. The trainee's rebuttal was a quote of Einstein's that things should be made as simple as possible, but not simpler. The trainee then asked the Boss to state Black-Scholes in a single sentence.

The Boss replied: Black-Scholes equation for a call option simply means that given that the call option moves as a percentage of the underlying stock (asset) price there is a chance (finite probability) that it will end up making money for the holder of the option.

He went on: as a trader, you should know that the call advances or declines with the stock as a proportion of the move in the stock and if this happens then in the absence of any other trade there is a distinct possibility (finite probability) that you will make money if you have bought that call. As to your phrase about "if nothing happens in the market", there is always something happening in the market. So, don't ever say that again. It was the trainee's time to get impressed.

I have had the opportunity to know both the trainee and the Boss quite well and over the years I have learnt a lot from them. I have learnt that mathematics, like the laws of physics, is a priori true. Two plus two is always four, just like the orbits of the planets of our solar system are all in a plane and elliptical in shape. It doesn't matter how we observe them or what experiments we perform. They will always be like that, just as they have been before us and will be so long after we are gone. However, financial markets are created by human beings and they are not invariant under human behaviour. The very fact that we participate in the buying and selling of stocks and commodities changes the mathematical construct of the market, if there is one, and such a construct is not sacrosanct.

I remember in one of the internal quarterly meetings the Boss had told a guy from the compliance and internal audit department that the only reason he had bought a certain option was because he couldn't find anyone to bet on a certain currency pair (FX contract).

When he saw the blank look on this guy's face he explained: you see if you can find someone to bet on an asset (currency pair in this case) and you can take his bet then all you need to do is to buy that particular asset in a certain proportion and you will never need to buy any call option. After about half a minute's silence just so that this guy (important as he was) doesn't panic, the Boss finally said, ok, ok, what I mean is a vanilla call is a long asset plus a short binary scaled by the strike and since I can't easily replicate a short binary times the strike for this FX contract, I am better off buying the call.

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