 # Understanding Option Greeks

## Theta | Vega | Delta | Gamma

Learn how to use covered calls to reduce the price of buying a call or to hedge for the downside potential of your existing stocks.

## Learn how to set up and profit from diagonal calendar spreads

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 (see  How much is an option worth?).

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.

• Gauge the likelihood that an option you’re considering will expire in the money (Delta).

• Estimate how much the Delta will change when the stock price changes (Gamma).

• Get a feel for how much value your option might lose each day as it approaches expiration (Theta).

• Understand how sensitive an option might be to large price swings in the underlying stock (Vega).

• Simulate the effect of interest rate changes on an option (Rho).

The two most important reasons for setting up a covered call:

• Reduce cost basis of buying a stock
• Hedge an existing stock portfolio if you already own 100 shares of a stock.
• Covered calls are profitable even if the stock down’t move
Covered calls are profitable unless the stock moves down below the break even price.

A covered call reduces the cost basis of buying a stock by accepting a premium for selling a put above the stock price.

If you were to sell the 105 put for a premium of 5 dollars.  The collected premium effectively lowers the cost basis of buying 100 shares of the stock at 100 dollars to buying the 100 dollars of shares at 95 dollars.  The break even price is now 95 dollars.

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The expected move can be calculated by adding the ATM call and the ATM put.  This is also how the options creators define a one standard deviation move.

ATM call + ATM put = expected move = 1 SD move

## Summary

Delta

• A measure of how sensitive the option is to changes in the stock price
• Roughly related to the % probability of profit
• A delta of 0.49 means that the stock will change 49 dollars for every 1 dollar change in the stock
• Also means that there is about a 49% chance that the option will end ITM
• Call deltas are positive + between 0-1
• Put deltas are negative
• The deeper you are ITM, the closer the delta will be to +1 or –1 ( I.e. it resembles the price of the underlying stock )
• Having a delta neutral portfolio can be a great way to mitigate directional risk from market moves

Gamma

If you are holding a long call with a given delta and the price goes up, you will want to roll your trade up eventually to capture higher gammas.  This is because as your stock increases in value, your delta are moving further and further from the ATM price;  increases in your option value will begin to decelerate.  By rolling the trade up, you are increasing your gamma accelerant.

Delta is the single most important factor in determining an option’s price

• Gamma can be thought of as the accelerant of Delta
• Higher Gammas will accelerate the underlying changes in Delta
• Gamma is highest for ATM options
• Delta for ATM options is approximately 0.5 or halfway between ITM and OTM options or halfway between 0 and 1 whether we are speaking of calls or puts
• Gamma decreases the further you are from ATM options ( whether ITM or OTM )
• Long options have positive gamma while short options have negative gamma
• A measure of how much delta will change give a 1 dollar change in the stock price
• A Gamma of .49 means that if the stock price changes by 1 dollar, the delta will change by .49
• Gamma is always highest at ATM options and decreases the further you are ITM or OTM
• So if you have an ATM call and the underlying goes up, the delta will quickly change toward a 1 delta
• Gamma sensitivity exponentially increases as expiration nears. Gamma is important to keep in mind when hedging deltas because low gamma positions require less maintenance than high gamma positions.

Theta

• Theta measures the rate of change in an options price relative to time. This is also referred to as time decay.
• A Theta of –0.11 means that the stock will lose 11 dollars of value for every day that passes
• There is a steep drop-off as you approach the end of a contract
• Theta values are negative in long option positions and positive in short option positions.
• Theta is a much smaller component of an OTM option’s price, the closer the option is to expiring.
• Initially, out of the money options have a faster rate of theta decay than at the money options, but as expiration nears, the rate of theta decay for OTM options slows and the ATM options begin to experience theta decay at a faster rate. This is a function of theta being a much smaller component of an OTM option’s price, the closer the option is to expiring.
•  Theta values are negative in long option positions and positive in short option positions.

Vega

• Measures how much the option will move in response to changes in IV
• If Vega if .08, then a 1% change in IV will increase by 8 dollars
• If there is a sudden drop in IV such as in earning, the Vega will drop dramatically ( eg .08 to .02 ) and therefore the option will only change by 2 dollars instead of 8
• is the greek metric that allows us to see our exposure to changes in implied volatility. Vega values represent the change in an option’s price given a 1% move in implied volatility, all else equal.

Beta

• Beta is the greek that allows us to weight our current positions with a designated benchmark.
• For example, you can beta weight a position to SPY, which is an extremely liquid product that emulates the S&P 500 index.
• It is important to note that beta statistics are calculated from five years of data, and the data is ever evolving.

## Understanding Vega? 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.

• Vega measures how the implied volatility of a stock affects the price of the options on that stock.

• Volatility is one of the most important factors affecting the value of options.
• 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.

• A drop in Vega will typically cause both calls and puts to lose value.
• An increase in Vega will typically cause both calls and puts to gain value.

Implied volatility is derived using a theoretical pricing model and solving for volatility.

Since volatility is the only component of the pricing model that is estimated (based on historical volatility), it’s possible to calculate the current volatility estimate the options market maker is using.

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.

• Vega measures how the implied volatility of a stock affects the price of the options on that stock.
• Volatility is one of the most important factors affecting the value of options.
• 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. Chart studies for both of these values exist within StreetSmart Edge®.
• A drop in Vega will typically cause both calls and puts to lose value.
• An increase in Vega will typically cause both calls and puts to gain value.

Vega is the Greek metric that allows us to see our exposure to changes in implied volatility.

Vega values represent the change in an option’s price given a 1% move in implied volatility, all else equal.

• Long options & spreads have positive vega.
• Example strategies with long vega exposure are calendar spreads & diagonal spreads.
• Short options & spreads have negative vega.
• Some examples are short naked options, strangles, straddles, iron condors & short vertical spreads.

When thinking about vega, we have to remember that implied volatility is a reflection of price action in the option market.

• When option prices are being bid up by people purchasing them, implied volatility will increase.
• When options are being sold, implied volatility will decrease.
• With that said, when being long options we want the price of the option to increase.
• When being short options we want the price of the options to decrease.
• That is why long options have a positive vega, and short options have a negative vega.

An increase in implied volatility will benefit the long option holder, as that indicates an increase in option pricing, hence the positive vega assignment.

A decrease in implied volatility will benefit the short option holder, as that indicates a decrease in option pricing, hence the negative vega assignment.

## Vega?

Since we normally hold a short vega portfolio as option sellers, we are exposed to volatility increases. We have to be careful with this exposure as volatility generally has velocity to the upside.

This means volatility can quickly spike up, as it usually has a negative correlation with the market, which tends to have velocity to the downside.

Managing our vega is important to ensure that we don’t have more exposure than we’re comfortable with from a portfolio perspective.

Vega: sensitivity to volatility

•

## What is Theta? 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.

Theta is the daily decay of an option’s extrinsic value. This metric is the cloudiest of all, as it assumes implied volatility & price movement are held constant. For this reason, it’s better to think of theta decay from the bigger scheme of things.

If we have positive theta, we’re on the right side of the coin. To obtain positive theta, we can sell options. All options with time left until expiration will have extrinsic value. As an option seller, this decay is a good thing. Let’s say we sell a put for \$1.00. To close the position, I need to buy back that same option. In order to realize profit, I need to buy the option back at a lower price. This is why theta is shown as a positive value for option sellers. The daily decay of an option price will help us realize that profit sooner.

If we have negative theta, we’re on the wrong side of the coin. To obtain negative theta, we would have to buy options. Having negative theta is not a fun feeling, as we are trading against the clock. The extrinsic value of our options will dissipate over time, which means we have to be directionally right quickly in order to see a profit, or we need implied volatility to expand more than theta will decay the option. This is why we always hedge our long options with a short option. We prefer long vertical spreads, calendar spreads, and diagonal spreads compared to long naked options, because we can eliminate a lot of the decay, if not all of it.

The most important aspect of theta to remember is that it assumes implied volatility & price movement are held constant. Markets move every second, so it is unrealistic to expect them to be frozen. We can’t look at our options and expect the value to decrease by theta every single day. While theta will come out of the option, price movement & implied volatility will change the value as well. As long as we’re on the right side of the coin (positive theta), we can rest assured that our option’s extrinsic value will get lower and lower as we reach expiration, which is one of the keys to success for an option seller.

## What is Delta?

Delta is the greek that helps us get a better understanding of our directional exposure. It also can be used to determine share equivalency, and as a proxy for calculating prob. ITM. It tracks the theoretical rate of change of an option’s price, given a \$1.00 increase in the underlying’s price. Strategies that are bullish will have a positive delta. Strategies that are bearish will have a negative delta.

Delta: The hedge ratio

• 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 0.40 means that the option’s price will theoretically move \$0.40 for every \$1 move in the price of the underlying stock or index.

Call options

• Have a positive Delta that can range from zero to 1.00.
• At-the-money options usually have a Delta near .50.
• The Delta will increase (and approach 1.00) as the option gets deeper in the money.
• The Delta of in-the-money call options will get closer to 1.00 as expiration approaches.
• The Delta of out-of-the-money call options will get closer to zero as expiration approaches.

Put options

• Have a negative Delta that can range from zero to -1.00.
• At-the-money options usually have a Delta near -.50.
• The Delta will decrease (and approach -1.00) as the option gets deeper in the money.
• The Delta of in-the-money put options will get closer to -1.00 as expiration approaches.
• The Delta of out-of-the-money put options will get closer to zero as expiration approaches.
• You also might think of Delta, as the percent chance (or probability) that a given option will expire in the money.

For example, a Delta of 0.40 means the option has about a 40% 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.

You also might think of Delta, as the number of shares of the underlying stock, the option behaves like.

A Delta of 0.40 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 40 shares of the stock.

Delta: Directional Exposure

If a long call option has a 0.30 delta, and the underlying increases \$1.00, that option should see an increase in price of \$0.30, all else equal (some other factors impact an option’s price, but we assume those are frozen for this example). If we saw the underlying decrease by \$1.00 instead, we would see the call option lose \$0.30, all else equal.

If a long put option has a (0.40) delta, and the underlying increases \$1.00, that option should see a decrease in price of \$0.40, all else equal. If we saw the underlying decrease by \$1.00 instead, the put would actually gain \$0.40 in value, all else equal.

It’s important to remember that buying an option does not always mean you’re bullish. As you see above, buying a put is actually a bearish strategy. Selling a put is bullish. When it comes to directional assumption with options, buying and selling are not synonymous with bullish and bearish like it is for stock purchases.

Delta: Share Equivalency

Delta can also be used as a way to add, subtract or neutralize deltas from being long or short stock. Each share of stock is 1 delta, so 100 shares of stock would equal 100 positive deltas. Each \$1.00 the underlying moves up would result in a gain of \$100. Some investors may want to adjust this exposure at certain times during the share ownership, and we can use options to do just that!

Let’s take a covered call for example, which is selling 1 call against 100 shares of stock. A short call is a bearish strategy, and therefore has negative delta naturally. Selling an out of the money (OTM) call with a delta of (0.30) would hedge our directional exposure by 30%! We would now have a net delta of 0.70, and no additional risk. We do cap my upside potential, but we reduce my loss potential if the stock price drops.

If we wanted to completely neutralize my delta temporarily, we could sell two at the money (ATM) calls at a delta of (0.50). This would net the delta out to 0, but we would be taking on more risk as one of the short calls would be uncovered.

It’s important to remember that deltas change, so in both of these examples if the stock price dropped the call deltas would decrease, reducing the overall hedge. Options can be a great way to fine tune directional exposure at any time.

Delta: Probability ITM Proxy

Delta can also be used as a proxy for estimating probability of being ITM. The two numbers are very similar, especially if volatility skew is low in a particular market. For example, if we’re looking for a 1 standard deviation option, which would be the 16% probability of being ITM, we can just look for the 16 delta option. It will likely be very close to the actual strike that would represent the 16% prob ITM, if it’s not that exact strike already!

Delta Neutrality

If you’re familiar with the show, you’ll notice the show hosts refer to being delta neutral a lot. This just means that they have various positions on (some bullish and some bearish) but their overall portfolio is pretty delta neutral. It can be very difficult to trade directionally, so we often choose to keep our deltas neutral. This means that if there are big directional moves in the market, our portfolio will be at less risk than if we were fully directional and wrong. We rely on theta decay, and implied volatility overstatement as our main drivers of long term edge, not directional trading.

## What is Delta?

Let’s take a covered call for example, which is selling 1 call against 100 shares of stock. A short call is a bearish strategy, and therefore has negative delta naturally. Selling an out of the money (OTM) call with a delta of (0.30) would hedge our directional exposure by 30%! We would now have a net delta of 0.70, and no additional risk. We do cap my upside potential, but we reduce my loss potential if the stock price drops.

If we wanted to completely neutralize my delta temporarily, we could sell two at the money (ATM) calls at a delta of (0.50). This would net the delta out to 0, but we would be taking on more risk as one of the short calls would be uncovered.

It’s important to remember that deltas change, so in both of these examples if the stock price dropped the call deltas would decrease, reducing the overall hedge. Options can be a great way to fine tune directional exposure at any time.

Delta: Probability ITM Proxy

Delta can also be used as a proxy for estimating probability of being ITM. The two numbers are very similar, especially if volatility skew is low in a particular market. For example, if we’re looking for a 1 standard deviation option, which would be the 16% probability of being ITM, we can just look for the 16 delta option. It will likely be very close to the actual strike that would represent the 16% prob ITM, if it’s not that exact strike already!

Delta Neutrality

If you’re familiar with the show, you’ll notice the show hosts refer to being delta neutral a lot. This just means that they have various positions on (some bullish and some bearish) but their overall portfolio is pretty delta neutral. It can be very difficult to trade directionally, so we often choose to keep our deltas neutral. This means that if there are big directional moves in the market, our portfolio will be at less risk than if we were fully directional and wrong. We rely on theta decay, and implied volatility overstatement as our main drivers of long term edge, not directional trading.

## What is Gamma? Gamma: the rate of change of Delta

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 \$.40, the Delta is no longer 0.40.

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 0.55.

This change in Delta from 0.40 to 0.55 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 and Delta approaches 1.00.

## What is Implied Volatility? Though not actually a Greek, implied volatility 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:

Implied volatility is derived using a theoretical pricing model and solving for volatility.

Since volatility is the only component of the pricing model that is estimated (based on historical volatility), it’s possible to calculate the current volatility estimate the options market maker is using.

Higher-than-normal implied volatilities are usually more favorable for options sellers, while lower-than-normal implied volatilities are more favorable for option buyers because volatility often reverts back to its mean over time.

To an options trader, solving for implied volatility is generally more useful than calculating the theoretical price, since it’s difficult for most traders to estimate future volatility.

Implied volatility is usually not consistent for all options of a particular security or index and will generally be lowest for at-the-money and near-the-money options.

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.

Implied volatility (commonly referred to as volatility or IV) is one of the most important metrics to understand and be aware of when trading options.

In simple terms, IV is determined by the current price of option contracts on a particular stock or future. It is represented as a percentage that indicates the annualized expected one standard deviation range for the stock based on the option prices. For example, an IV of 25% on a \$200 stock would represent a one standard deviation range of \$50 over the next year.

What does “one standard deviation” mean?

In statistics, one standard deviation is a measurement that encompasses approximately 68.2% of outcomes. When it comes to IV, one standard deviation means that there is approximately a 68% probability of a stock settling within the expected range as determined by option prices. In the example of a \$200 stock with an IV of 25%, it would mean that there is an implied 68% probability that the stock is between \$150 and \$250 in one year.

## What is Implied Volatility?

Why is this important?

Options are insurance contracts, and when the future of an asset becomes more uncertain, there is more demand for insurance on that asset. When applied to stocks, this means that a stock’s options will become more expensive as market participants become more uncertain about that stock’s performance in the future.

When the uncertainty related to a stock increases and the option prices are traded to higher prices, IV will increase. This is sometimes referred to as an “IV expansion.”

On the opposite side of IV expansion is “IV contraction.” This occurs when the fear and uncertainty related to a stock diminishes. As this happens, the stock’s options decrease in price which results in a decrease in IV.

In summary, IV is a standardized way to measure the prices of options from stock to stock without having to analyze the actual prices of the options.