Options Theory: The Whiz-Bang Option Pricing Machine
September 10, 2017
Last Update: August 2021
If you’re going to befriend options and attempt to tap-in to their profit-giving ways, you must of necessity learn their quirks. How do they behave and, perhaps more importantly, why do they act so? This will be the topic of today’s missive.
Options are instruments, yes, but they are also organisms. Living, breathing things that change over time. But unlike, say, a teenager that behaves unpredictably, options operate in a consistent, predictable manner. And thank goodness for that! Can you imagine trading a product that didn’t act as expected? One whose behavior was as fickle as the weather?
But no, option contracts operate as designed all the time, every time. It simply requires an understanding of their innards. In a moment we’ll commence with the dissection.
Options were the brainchild of three mathematical geniuses: Fisher Black, Myron Scholes, and Robert Merton. They had in their minds the idea of creating a perfect product, a derivative that could be used for hedging and speculation. One that allowed for a more sophisticated game of investing involving considerably less risk.
For days they toiled in their laboratory, testing and trying. But eventually, their financial Frankenstein came fully alive. A peek into his anatomy would reveal six parts and six parts only: stock price, strike price, time to expiration, volatility, dividends, and interest rates. A change in any one of these variables is what drives the behavior of Franky.
If you want to be a top rate options aficionado I suggest you memorize all six. They are the inputs to what eventually became known as the Black-Scholes Model. If the Frankenstein metaphor is too messy, or if all this talk of anatomy and dissection conjures up stinky images of biology class and frogs, then allow me to switch metaphors.
The Black Scholes Model is a machine designed to create an option’s premium (aka an option’s cost or an option’s price). You put the six inputs into the machine and out pops an option’s premium. And since there are two option types – call and put – the machine is built to create a price for either one. Just switch the lever.
Math lovers may want to crack open the machine to see how exactly the Black-Scholes model ticks, but really, that’s unnecessary. You don’t need to know the complex formulas to trade options successfully. A basic understanding of how a change in the inputs impacts the output will suffice. Before we get to that, let’s change the graphic and state the inputs and output in terms we will use moving forward.
I’ve color-coded each input and since the output is a combination of all of them, it includes every color. Like a rainbow!
Now, let’s look at how a change in each input modifies the premium amount. Remember that call options give you the right to buy a stock and put options give you the right to sell a stock.
Stock Price
The higher the stock price, the higher the option premium. A call/put on a $500 stock is more expensive than one on a $50 stock.
- As the stock rises, calls get more expensive while puts get cheaper.
- As the stock falls, calls get cheaper while puts get more expensive.
Strike Price
This variable is fixed and does not change over the life of an option. It is the price at which the option owner has the right to buy/sell the underlying stock.
- The lower the strike price the more expensive the call and the cheaper the put.
- The higher the strike price the more expensive the put and the cheaper the call.
Time
- The more time to expiration, the more expensive the call/put
- The less time to expiration, the less expensive the call/put
- As time passes, all options lose value. This is a phenomenon known as time decay.
Volatility
Think of this as how much the stock is expected to move between now and expiration.
- The higher the volatility, the more expensive the call/put
- The lower the volatility, the less expensive the call/put
Dividends
When a stock pays a dividend (this is a distribution of profits to shareholders) its share price typically falls by the amount of the dividend. To be efficient, the Black-Scholes Model takes this into account.
- Since a dividend payment reduces the forward price of a stock, it lowers call premiums while raising put premiums.
- High dividend-paying stocks have cheaper call options and more expensive put options.
Interest Rates
The impact of interest rates is minimal so I’m going to keep this explanation short and sweet.
- The higher the interest rate, the more expensive the call and the cheaper the put.
- The lower the interest rate, the more expensive the put and the cheaper the call.
If you really want to sink your teeth into option pricing, I suggest two things:
First, become a pro member of Tackle so you can get free access to the Options 101 video series. If you’re already a pro member you’ll find the class under the Learning Center. It includes hours of instruction on what makes options tick.
Second, play around with an option pricing calculator to experiment with how changing the different inputs impacts an options premium.
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Useful Info to understand the options pricing..
Great explanation of option pricing Tyler. I must admit I did geek out on the Black-Scholes model for two seconds when Matt introduced options to me 🙂