Understanding option pricing, whether it be a single position or a multi-leg option trade, can be challenging with all the different aspects of the option pricing model. Several factors affect the options price, from stock direction, to time, to volatility changes, to interest rate changes, all of these factors are consistently influencing and options pricing and are calculated using the black scholes model.
To get a better understanding of how these factors influence option pricing, traders referred to terms known as Greeks. These include the delta, gamma, theta, and vega. The Greeks provide a quantifiable means to measure an options pricing sensitivity to the factors that influence them. Although often confusing for new traders, option Greeks are the best means to make sense of a trader’s potential risk and reward with the trade.
Delta
The delta is the main Greek you need to be concerned with, so if you are just going to learn one Greek right now, this is the one to pay the closest attention to. The delta will have a value anywhere from 0 to 1 for calls and 0 to -1 for puts. Your delta will reflect the increase or decrease in the pricing of the option as it relates to a $1 movement in the stock, also known as the theoretical change in the option pricing as it is affected by stock movement.
For example, one share of stock always has a delta of 1, so 100 shares of stock in ABC will have a positive deltas equal to 100. If we own 100 shares of ABC and the stock moves up $1, then we make $100.
Options that are out of the money will have a delta less than .5 while options in the money will have a delta than greater than .5. Options right at the money will have a delta of exactly .5 (Not including interest and dividends).
At this point, you may be starting to see the delta is also the probability the option will finish in the money. For example, if ABC is trading for $50 and you buy the 50-strike price call, the option theoretically has a 50/50 chance of finishing in the money. It could go up and finish in the money, or it could go down and finish out of the money.
If we were to buy a 40-strike price call with the stock trading $50, this has a much better chance of finishing in the money. The stock would have to drop $10 to finish out of the money, so this would have a higher delta. Depending on the time to expiration and volatility, this call could have a delta of .85.
If we were to buy a 60-strike price call, the stock would have to increase in value $10 to finish in the money, the probability of that happening is much less depending on time to expiration and the volatility of the stock, this option might have a delta of only .15.
Delta is essential as it gives us a real-life probably that our option will finish in the money or not, and from this, we can make strategic plays.
Delta also tells us how much money we are going to make or lose in a $1 swing in the stock. If we buy one option contract of the 50-strike call for $2.50 and the stock trades up $1 the next day, we will make $1 times the delta for a profit of $.50. Being that one contract settles into 100 shares, this is a $50 profit.
100 shares x $1 stock change x .5 delta = $50 profit
In the real world, the delta is referred to as in percentage format. So, a delta of .15 we refer to as a delta of 15. An option with a delta of 1 we refer to as a delta of 100. Think of this as how batting average is kept in baseball. If someone is referred to as batting 300, what they really mean is that they are batting .300, same thing with delta. So, moving forward when I say a delta of 30, I mean .30.
Let’s look at an out of the money position. If I were to buy 20 contracts of the 60-strike price of ABC for $.30, how much money would I make if the stock traded up $3 the next day?
2000 shares x $3 stock change x 15 delta = $900 profit
Remember, a 15 delta is a .15 delta, but written in percentage format by default.
As the stock trades up, the delta will increase for call and decrease for puts. As the stock trades down, the delta will increase for puts and decrease for calls.
Gamma
Like the delta, the gamma is written in percent format and reflects the rate of change in the delta with a $1 movement in the stock. As we just saw with delta, if the option is deep in the money, it has a delta of close to 100, and far out of the money has a delta of close to 0, gamma is what measures this change as the stock moves.
As we know with delta, gamma is also always changing; it will have its highest value right at the money and decrease in value as you get farther away from the money. For example, an ABC 10-strike price put would have little gamma if the stock was trading $50. The stock could move up or down $10, and the put is still so far out of the money it would not change the delta of nearly 0.
Whether you are trading calls or puts, you always add gamma to the old delta as the stock rises and subtract the gamma from the previous delta as the stock drops.
If an option has a gamma of 5 for each $1 increase or decrease in the stock price, my option will gain or lose deltas.
What you need to understand about gamma is that the more the stock trades in your favor, the more money you make, and as the stock trades against you, the more money you lose.
If we buy a one ABC 45-strike price put with the stock trading $50, we would have a delta of about -30. If the stock trades down $1, I make $30.
100 shares x -$1 stock change x -30 deltas = $30
But my delta is now 35 due to the gamma change, so if the stock trades down another dollar, I now make $35, and my delta is now -40. It will continue like this until the delta is so far in the money or out of the money that the gamma does not affect the delta anymore as 100 is the max delta.
Theta
Theta is the measurement of the options’ time decay. Options are decaying assets, they all have expirations, and when that expiration day comes, the option will either have value or have no value, it is one or the other. More time adds more value to the option. Theta is the rate at which an option loses its value through the passage of time.
For example, an option that is worth $2.50 today with a theta of .05 will be worth $2.45 tomorrow and $2.40 the day after that.
Long term options have a theta of almost 0. Because they have so much time, they do not lose value from day to day. Theta goes up substantially as options near expiration losing more and more value with each passing day. As a general guideline, options begin to decay quickly at about 56 days out from expiration.
As you can see in the graph above, the closer we get to expiration, the more decay in the option, with most of the decay coming in the last 30 days.
Vega
Vega is the measure of the change in the implied volatility of the option. The vega of an option is shown by a point change in theoretical value for each percentage point change in volatility. So, what does that mean? Basically, an increase in volatility means an increase in the option price and a decrease in volatility results in a decrease of an option price.
It does not matter if you are dealing with calls or puts, when you encase volatility the price goes up and when you decrease the price goes down.
Vega will decrease as expiration approaches; less time means a lower chance of stock movement. A six-month option will have a greater vega versus a one-month option and will be more sensitive to a change in volatility.
Vega is the Greek letter you need to be least concerned with. However, at some point in your trading career, you will notice a swing in the stock, but the option price will not change as much as you had calculated. This is because volatility to counteract the change in the stock price.
Conclusion
The Greeks are an essential tool to help measure and options risk and reward. The Greeks are confusing for all new traders, but once you have a good grasp of how they work, you have a better understanding of how to implement the Greeks with your option strategies. To have the best chance to profit with the options market, every trader should understand all aspects of the trade and how the trade could potentially lose money or make money.
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