Many options trading beginners struggle with the heavy math jargon involved. All the talk of Deltas, Gamma, implied volatility etc is enough to persuade many who were glad to leave algebra aside at school that options trading is not for them.
Well, here’s a simple way of working out where an option will go given a certain change in conditions, without the need for any of this knowledge. It’s actually a throwback to the origins of options pricing models, in the 1970s. So before I get into how this works, a bit of a history lesson…
Advanced traders tend to take it for granted now that the value of an option . Give us a set of variables and we can plug them into an excel spreadsheet/online calculator and come up with ‘the’ price of an option. However it wasn’t so long ago that there were no agreed valuation methods. Indeed up until the mid seventies the amount you’d pay for, say, an option to buy AAPL at $450 in one month’s time (with AAPL at, say, $440) was a matter intense academic debate.
This was to change with the publication of “The Pricing of Options and Corporate Liabilities” by the academics Fischer Black and Myron Scholes in 1973. This, and further work by Robert Merton, set up the most popular and widely used model, the Black-Scholes model. This is what most of us use today, whether we know it or not, and allows us to determine the value of an option given just five variables: stock price, time to maturity, strike price, volatility and interest rates.
But why is this rather dry academic history of use to we practical trader types? Well the background of how they came up with this formula provides a really good way for those who struggle with the math inevitably involved in these models to predict options price behavior.
The Metal Bar And The Heat Equation
Fischer Black, the senior member of the group, was an engineer by profession. His insight was that an option price acts in a similar way to something he knew how to model: heat passing through a metal bar.
Imagine a metal bar, which starts to be heated from one end. What would affect the temperature of the bar at a given point, after a given time? In particular, what would be the factors that would determine this temperature.
Well I think we can say that the temperature of the heat source would effect it, as would its distance from the point we are assessing. The amount of time the bar had been heated would also be a key factor. And how good a conductor the particular metal was. And, perhaps less obviously, how good the surrounding atmosphere was at cooling the bar.
Indeed Black knew how to take each of these factors and produce an exact prediction of the temperature at a particular point in time for a particular spot on the bar: the ‘heat equation’ was a standard part of the engineering syllabus.
Black realised that you could model an option price (‘temperature’) if you substituted ‘heat of the source’ with stock price, the distance from this source as the strike price (or, to be more accurate, its distance from the stock price), time to maturity for the length of time the bar had been heated, interest rates for external ‘cooling’ and volatility for conductivity. This provided a great model for how options pricing (or, again more accurately, the time value in an option) worked.
So if you’re ever stuck on working out how a factor affects option pricing try to think of that bar. If you want to know, say, how an out of the money call option behaves as it moves higher, think of that metal bar: would the temperature rise or fall as you moved away from the source (stock price)? Fall of course.
Or if volatility fell (the metal became less able to conduct heat) isn’t it easy to now see that the option price (temperature) would fall too?
Or interest rates (cooling ‘ability’) rise? Then the options price (temperature) falls.
Although this seems a rather silly example it’s actually how Scholes and Merton (but sadly not Black, he died before the award) won a Nobel Prize for Economics. Plus if it helps you understand the way options pricing moves with changes in the various key factors then who cares.
There’s just one warning. Don’t take the pricing produced by the Black Scholes model without understanding its weaknesses. Soon after the theory was made public a devastating article was written by an eminent professor concerned that traders were using the formula without understanding its many flaws. Volatility isn’t as constant as the conductivity of a particular metal. It was only designed for European Options (those that can only be exercised on expiry) not the American ones (this that can be exercised at any time to expiry) most commonly traded. It assumes a nice neat distribution of returns, ‘log normal’ distribution, which experience has shown to underestimate extreme risks. And so on.
And the writer of this article? Fisher Black just before he died. We should heed his advice: the fact that we now have a great model to price options, including this qualitative way of determining options behavior, doesn’t mean that we have perfect knowledge.
Let the buyer (and seller) of options beware.