How We Decode Options Pricing  | BY Keith Kaplan
CEO, TradeSmith |
A few weeks back, we took a short break from our options education series – what I’ve come to affectionately call “climbing the learning wall.” Today, we continue it. When we last left off, we talked about “moneyness,” an essential concept to grasping options profitability. (I also promised to discuss my personal favorite way of trading options… selling them, not buying them. Jogging my memory a bit, it turns out I’ve already showed you that. Pardon the lapse… I’ve written a lot over the years!) So today, we’ll look at another fundamental options concept that you should know… some of. Yup. Call it educational sacrilege if you want, but in my practical opinion, you don’t need to know every single numerical factor of every options trade you’ll ever make. It’s a bit like how we all drive cars, but a slim fraction of us know even the beginning of how they work. You need to know enough to shift the gears, replace the wiper blades, gas it up and pump up the tires. But you probably don’t need to know how to change the oil or replace the brake pads. What I’ll show you today is like that. It’s good to know why you need to do these things, but by no means do you HAVE to do them yourself… I’m talking about the “Greeks” of options trading. This is shorthand for five factors, represented by letters of the Greek alphabet, that impact options pricing. They are: - Delta – which you can use to determine how likely an option is to expire in the money.
- Gamma – the measure how much the Delta will change as the stock price changes
- Theta – a measure of time decay, or how much value options lose as they approach expiration
- Vega – how sensitive the option is to a stock’s implied volatility
- Rho – the measure of how interest rates impact options prices
You’ll notice only two of the above Greeks are bolded (and one other phrase, which we’ll touch on briefly today and in-depth another day.) That’s because these three concepts are the only ones you really need to understand when you want to trade options. This isn’t to say the rest aren’t of any use. They just don’t change all that much in the short term, and don’t really have a big impact on how you trade until you’re looking at more advanced strategies. So, without further ado, let’s cover the top three Greeks concepts you should understand to choose and manage your options trades “by hand”… How to Decode Options Prices – Starting with Delta Above, I told you that you can use Delta to determine the likelihood an option will expire in the money. It does that by measuring how much an option’s price will change for every $1 rise in the underlying price. Call options have positive delta, since they gain value as a stock rises and they get further from their at-the-money price. Conversely, put options have negative delta, so they lose value when a stock rises and gain value when it falls away from the at-the-money price. The lower the delta, the lower the likelihood an option will close in the money… and also the greatest profit potential if the underlying price moves higher quickly. For call options, delta goes from 0 to 1, and at-the-money options have 0.5 delta. For put options, delta goes from -1 to 0, with at-the-money options at -0.5 delta. The further in the money a call option goes, the closer its delta gets to 1. Similarly, the further in the money a put option goes, the closer it gets to -1. And as call and put options go further out of the money, the deltas approach zero. Take a look at this option chain for Apple (AAPL). These are the call options expiring this Friday, Oct. 4. 
Source: Thinkorswim by Charles Schwab With Apple’s current price at $231.55, that places the at-the-money split in between the $230 and $232.5 strike prices, which are listed on the right side. The purple sections highlight in-the-money strikes, while the black sections denote out-of-the-money strikes. Now, follow the delta column on the left. You can see that the further in the money an option strike is, the higher the delta for call options. And vice versa. Notice also how, when you look right around the break between the purple in-the-money options and the black out-of-the-money options, the deltas are close to 0.5. At-the-money options tend to have deltas right around that level. So, if you own, say, the $230 call option expiring this Friday for AAPL, every $1 move higher in the share price will cause that option’s value to rise by $0.61. But what’s important to understand here is how much the delta changes between the strike prices. For example, the difference between the at-the-money split strike prices, $230 and $232.5, is 0.16. However, further up, the difference between the $222.5 and $225 deltas is only 0.07. This changing rate of delta is what’s referred to as gamma. Gamma is the rate of change in delta for every $1 increase in the underlying asset. Think of it like this: If an options contract is a car, delta is the speed and gamma is your acceleration. Why Is Delta Important? You can think of delta as the potential of the number of shares you control. But wait, doesn’t every option contract control 100 shares of stock? Yes, that’s true. If you exercise that contract, you’re buying or selling 100 shares. However, when it comes to trading options for the difference in premium, it’s important to look at the delta to understand how much price gain is in store for you. A call option with 0.5 delta technically controls 100 shares of stock. But it doesn’t act like that. It acts like it controls 50 shares of stock. Here’s an example using the options chain for the SPDR S&P 500 ETF (SPY). 
Source: Thinkorswim by Charles Schwab The $572 call option has a delta of 0.48. Let’s assume the SPY moves higher by $1. From the last price of $571.21, that should mean the new price of the $572 call option would match the current price of the $571 call option. Here’s how that math works: $572 – $571 = $1 change x 0.48 delta = $0.48 However, the difference in price between the $572 call option and $571 call option is $0.52. Why don’t the two match exactly? Two reasons. First, the delta changes as the price of the underlying asset changes. So, it’s probably more accurate to use a 0.50 delta for our calculations, since that’s the average of the two deltas. Second, and more importantly, option prices are also determined by implied volatility. And believe it or not, those two options have different implied volatility, even though they are so close together. The $572 call option has an implied volatility of 17.34%, while the $571 call option has an implied volatility of 17.52%. If you did the calculations using vega, the Greek for measuring changes in implied volatility, you would find out that it contributes $0.04 to the option’s price. So, adding the impact of delta and vega (implied volatility) gives us $0.48 + $0.04 = $0.52, the exact difference between the two option prices. Pretty neat, right? There’s much more to say on implied volatility, enough to fill an entire issue of TradeSmith Daily. It rises and falls pretty dramatically around big events like earnings reports, stock splits – and, of course, the biggest event of all for an options contract: its expiration. So, we’ll cover that in a future issue. A Word on Gamma I briefly touched on gamma earlier. Now I want to dig a little deeper. This chart shows the gamma (blue line) and delta (red line) of a call option. The orange line denotes where the stock’s current price is (the at-the-money line): 
Source: TradeSmith Let’s start with that red delta line. As we discussed earlier, call options’ delta approaches zero the further out of the money you go and approaches 1 the further in the money you go. That’s what creates the S-shaped delta curve. The slope of that curve is gamma. And you can see that when an option is at the money, the curve is at its steepest point. However, as you move further away from the stock’s current price, that slope decreases. That’s why gamma has a bell-curve shape with its peak at the money. This tells us that the rate of change for delta is greatest at the money and decreases as you move away from the stock’s current price. Using the car analogy, the car’s acceleration is greatest at the current stock price, and that acceleration decreases as you move further in or out of the money. Why Delta and Gamma are the Two Key Greeks If you learn only two options Greeks, make them delta and gamma. Delta tells you how exposed your option is to changes in a stock’s price. And since stocks tend to move around, this is extremely important – especially if your strategy actually depends on it not moving too much. That’s something we do a lot at TradeSmith when we sell options for income. Gamma, meanwhile, shows you how much delta could change as a trade works with you or against you. I recommend you take some time and pull up a few option chains. Model out different options strategies (long and short options, spreads, etc.) and see how delta changes. And once you’ve got your eye on a particular options contract, you can pull it up anytime in TradeSmith Options360 and visit the Statistics tab to monitor how the delta and gamma are reading, along with our ROI and Probability of Profit (POP) projections for your trade: 
Then, email me at feedback@TradeSmithDaily.com with any questions you might still have on the subject. I’ll look to publish my responses in a future issue, if we think they’ll be helpful for your fellow readers. All the best,  Keith Kaplan
CEO, TradeSmith | 
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