Understanding the Greeks
Greeks, including Delta, Gamma, Theta, Vega and Rho, measure the different factors that affect the price of an option contract. They are calculated using a theoretical options pricing model.
Since there are a variety of market factors that can affect the price of an option in some way, assuming all other factors remain unchanged, we can use these pricing models to calculate the Greeks and determine the impact of each factor when its value changes. For example, if we know that an option typically moves less than the underlying stock, we can use Delta to determine how much it is expected to move when the stock moves $1. If we know that an option loses value over time, we can use Theta to approximate how much value it loses each day.
Let's dive into the Greeks a bit more!
The first Greek is Delta, which measures how much an option's price is expected to change per $1 change in the price of the underlying security or index. For example, a Delta of 0.50 means that the option’s price will theoretically move $0.50 for every $1 move in the price of the underlying stock or index.
You can think of Delta, as the probability that a given option will expire in the money. For example, a Delta of 0.50 means the option has about a 50% chance of being in the money at expiration. This doesn’t mean your trade will be profitable. That of course, depends on the price at which you bought or sold the option.
Also, you might think of Delta, as the number of shares of the underlying stock, the option behaves like. A Delta of 0.50 also means that given a $1 move in the underlying stock, the option will likely gain or lose about the same amount of money as 50 shares of the stock.
Gamma measures the rate of change in an option’s Delta per $1 change in the price of the underlying stock. Since a Delta is only good for a given moment in time, Gamma tells you how much the option’s Delta should change as the price of the underlying stock or index increases or decreases. If you remember high school physics class, you can think of Delta as speed and Gamma as acceleration.
Let's walk through the relationship between Delta and Gamma:
Delta is only accurate at a certain price and time. In the Delta example above, once the stock has moved $1 and the option has subsequently moved $.50, the Delta is no longer 0.50. As we stated, this $1 move would cause a call option to be deeper in the money, and therefore the Delta will move closer to 1.00. Let's assume the Delta is now 0.65. This change in Delta from 0.50 to 0.65 is 0.15—this is the option’s Gamma.
Because Delta can’t exceed 1.00, Gamma decreases as an option gets further in the money (ITM) and Delta approaches 1.00.
Theta is an old person, the closer they get to "expiration" their value decays. Theta measures the change in the price of an option for a one-day decrease in its time to expiration. Simply put, Theta tells you how much the price of an option should decrease as the option nears expiration.
Since options lose value as expiration approaches, Theta estimates how much value the option will lose, each day, if all other factors remain the same.
Because time-value erosion is not linear, Theta of at-the-money (ATM), just slightly out-of-the-money and in-the-money (ITM) options generally increases as expiration approaches, while Theta of far out-of-the-money (OOTM) options generally decreases as expiration approaches.
Vega measures the rate of change in an option’s price per 1% change in the implied volatility of the underlying stock. While Vega is not a real Greek letter, it is intended to tell you how much an option’s price should move when the volatility of the underlying security or index increases or decreases.
More about Vega:
Neglecting Vega can cause you to overpay when buying options. All other factors being equal, when determining strategy, consider buying options when Vega is below “normal” levels and selling options when Vega is above “normal” levels. One way to determine this is to compare the historical volatility to the implied volatility.
Rho measures the expected change in an option’s price per one percentage point change in interest rates. It tells you how much the price of an option should rise or fall if the risk-free interest rate (U.S. Treasury-bills) increases or decreases.
More about Rho:
Rho is generally not a huge factor in the price of an option, but should be considered if prevailing interest rates are expected to change, such as just before a Federal Open Market Committee (FOMC) meeting.
Long-Term Equity AnticiPation Securities® (LEAPS®) options are far more sensitive to changes in interest rates than are shorter-term options.
You can see the effects of Rho by considering a hypothetical stock that’s trading exactly at its strike price. If the stock is trading at $25, the 25 calls and the 25 puts would both be exactly at the money. You might see the calls trading at a price of $0.60, while the puts may trade at a price of $0.50. When interest rates are low, the difference will be relatively small. As interest rates increase, this difference between puts and calls whose strikes are equidistant from the underlying stock will get wider.
Though not actually a Greek, implied volatility (IV) is closely related. The implied volatility of an option is the theoretical volatility based on the option’s quoted price. The implied volatility of a stock is an estimate of how its price may change going forward. In other words, implied volatility is the estimated volatility of a stock that is implied by the prices of the options on that stock.
Key points to remember:
Since it’s difficult on your own to estimate how volatile a stock really is, you can watch the implied volatility to know what volatility assumption the market makers are using in determining their quoted bid and ask prices. By comparing the underlying stock’s implied volatility to the historical volatility, you can sometimes get a good sense of whether an option is priced higher or lower than normal.
Chris the Miss - Option Tendies Creator. Enjoy the community!
Great information! I heard a great analogy from Josh @ THE TRADING FRATERNITY. Options can be very volatile and you can earn quick cash or lose all your cash. The goal is to budget and manage your cash. It is like a scuba diver. The deeper you go, the more money you make; BUT if you don't manage your oxygen (cash balance) you can get clapped and drown. Take small profits when you can, build positions and be content as a new trader (speaking to myself) with small gains over time and let TIME be your friend. Trying to YOLO demon everyday will lead to getting clapped and your rent not getting paid. I sound like Nate the Great haha!