Article Summary:
- Options are much more complex than stocks and, as such, require different measures of risk – the greeks.
- Option greeks are a set of terms used to describe the risk associated with options trading. They include Delta, Gamma, Theta, Vega and Rho.
- Delta measures the rate of change in option price in relation to changes in the underlying asset; Gamma measures how quickly Delta will change as the stock moves; Theta measures how quickly an option’s value erodes over time due to the passage of time; Vega measures how much an option’s price will move when volatility increases or decreases; and Rho is used to measure the sensitivity of an option’s price to changes in interest rates.
Introduction
While stock investors only have to deal with the risk of falling stock prices, options traders have many other risks. Because options are more complex than stocks and other delta-one products, options traders had to develop various measures of risk: the Greeks.
The Greeks are risk measures that describe how an option’s price will move relative to certain variables such as time, volatility, and underlying prices. This article focuses on introducing and discussing each of the five option Greeks in more detail so that readers can better understand their importance in options trading.
Delta
Delta is the most commonly used of all options Greeks and measures the rate at which an option’s price changes relative to a one-dollar change in the underlying asset’s price. For example, if a call option has a delta of 0.5, its price will increase by 50 cents when the underlying asset’s price increases by one dollar. Similarly, if a put option has a delta of -0.2, its price will decrease by 20 cents when the underlying asset’s price increases by one dollar. Stocks and futures are described as “delta-one” products because they have a delta of 1; traders earn $1 for each dollar the stock price increases.
Call options are long delta, meaning their delta values are positive. Their profit and loss are positively correlated with increases in stock price. Put options are short delta; they benefit when stock prices fall. Conversely, a short call position is short delta, while short puts are long delta.
While Delta is the most commonly used Greek, it is also the most misused by options traders. Many traders use delta as the probability that an option will be in the money at expiration. Not only is delta not this probability, but even the correct formula —N(d2)— for “probability ITM” that brokers use is derived from a model such as the Black Scholes. The Black Sholes uses implied volatility (which often differs from realised volatility) and assumes stock prices are random.
Delta is one of the least important Greeks for many because of how easily traders can hedge it. Traders can turn a long put into a long call by buying 100 shares. A short call becomes a covered call by purchasing stock as well; a covered call is identical to a short put. Market makers buy and sell options, frequently hedging by buying and selling shares. Many volatility traders hedge their options positions to be delta neutral and avoid exposure to the direction of the stock price.
Gamma
Gamma is a greek that indicates how much delta will change for every one-dollar move in the underlying asset’s price. It measures an option’s convexity. Gamma is essential for volatility traders because it allows them to make money regardless of which direction the stock price moves.
Consider a straddle with one gamma and no delta. If the stock price increases by $10, the straddle will have moved from 0 to 10 delta. We can estimate (by averaging 0 and 10) that the straddle had 5 Deltas on average while the stock price was moving, so the straddle’s profit is about $50. The same thing can happen in reverse. If the stock price decreases by $10, the straddle will have -10 Deltas. Using the same logic (average -5 Delta, -$10 move), we can see that the straddle also makes $50 when the stock price decreases. From this example, we can see how an option’s Gamma is important to options traders. Those who want to bet on the volatility of a stock depend on the Gamma of an option for their profits.
Long options (both calls and puts!) are long gamma; they gain delta as the stock price increases and lose delta as the stock price falls. This means that volatility is great for option buyers, who profit from being long gamma. Conversely, short options positions are short gamma; they lose delta when the stock price increases – we can see that volatility hurts option sellers.
It’s common for retail traders to recommend selling 45 DTE options and repurchasing them around 20 days before expiration because of “gamma risk”. As options approach expiration, options near the money get more Gamma. Small moves in the stock won’t affect the delta of long-dated LEAPS, but 30 Delta weekly options can quickly become 50 or 80 Delta after a small move. This is dangerous because the increased Delta can hurt short-term options sellers, especially if they don’t hedge.
Theta
Theta refers to time decay – meaning that all options eventually expire no matter their intrinsic value – and measures how much an option’s value decreases over time as expiration approaches. For example, if a particular option has a negative theta of -10, its value would drop by 10 dollars daily until expiration if all other things remain equal (delta being positive).
Because gamma is reasonably low for long-dated options but much higher for short-term options, long-term options have very little theta exposure. Still, theta is much higher as expiration approaches.
Theta isn’t inherently good or bad for options traders; it’s just a feature of the option. When traders buy gamma by purchasing an option, they have to pay theta, but they’re given the ability to make money from any directional move. This is similar to paying rent for an apartment – it’s okay if it is big enough.
Long options positions have negative theta; with all else equal, their options decay in value over time. Conversely, short options positions are long theta, as their options cost less to repurchase with every passing day.
Gamma and Theta are the critical Greeks during “shorter term” volatility trades. Volatility traders who buy Gamma are betting that the stock will be more volatile than the market’s implied volatility, who would then earn more profits from gamma than they have to pay in theta. Similarly, volatility traders who sell Gamma are betting they will make more in theta than they lose from gamma.
Vega
Vega is crucial for measuring volatility risk because it captures an option’s sensitivity to implied volatility (IV) movements, often due to different events such as earnings announcements or economic reports. For instance, if an option has a Vega of 10, its value will increase by 10 dollars when IV rises by 1 point; similarly, it will decrease by 10 dollars when the IV decreases by 1 point. An increase in implied volatility causes an option’s value to increase; when traders expect the stock to be more volatile in the future, there is more opportunity to profit from gamma. As a result, traders begin bidding up the prices of options. Vega essentially measures this effect.
Vega is the highest for options with a long time to expiration. Therefore, an extra percentage point of volatility will make little difference over the short life of a weekly option. However, an additional percentage point of volatility matters for options with several months to expiration; the small amount of gamma profits adds up over time.
Vega is positive for long options positions; implied volatility increases when the market believes there will be greater Gamma profits in the future, and the value of options increases. On the flip side, short options are short Vega. Because options sellers don’t want to be hurt by gamma and volatility, an increase in implied volatility is terrible news for them too.
Vega is the Greek most important for “long-term” volatility trades. Volatility traders who believe that implied volatility for LEAPS is too high or too low are typically hoping that the rest of the market notices this and pushes prices toward where they should be. Otherwise, they would have to hold these options for more than a year, collecting theta or profiting from Gamma bit by bit.
Rho
Rho is an option Greek that measures how the value of an option changes when interest rates change. For example, if an option has a rho of 10, its value will increase by 10 dollars when interest rates rise.
Call options have positive rho since the option to buy stock later is more important during higher interest rates. On the other hand, put options have negative rho since higher interest rates mean that the cash you receive for the stock is less valuable in the future.
However, Rho is typically only important for long-term options; their effect is rarely felt in options other than LEAPS.
Conclusion
In conclusion, it is important for options traders to be aware of the different Greeks and how they affect their trades. For example, gamma and Theta are most important during shorter-term volatility trades, while Vega and Rho become more relevant when trading long-term options like LEAPS. With this knowledge at hand, you’ll be able to understand how to structure trades when you identify inefficiencies in the market.
As with anything else, practice makes perfect – and the Greeks are no exception. So spend some time analysing options and understanding how different Greeks affect the price of an option, and you’ll soon be ready to take your trading skills to the next level.
Finally, it’s important to remember that even if you understand the Greeks, things may only sometimes go according to plan. The market is constantly changing, so managing risk is vital to ensuring that losing trades are manageable for your bottom line. That means having a clear strategy before executing any trade and knowing when it’s time to exit a position – regardless of whether or not it’s in line with your initial expectations.