# Memory Tricks for Options Greeks Like Delta, Gamma and Vega

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Options are complex instruments that can swing sharply in value. Traders may find the moves confusing, so this article will help explain key “Greeks” — some of the most important factors impacting the price of options.

Greeks are Greek letters used in complicated mathematical models. (They’re essentially variables in bigger formulas.) We’ll cover four of the most important Greeks to see how they impact the value of calls and puts. We’ll also provide memory tricks to help investors remember how they work.

## Delta

Delta is perhaps the most important Greek because it describes how calls and puts track the price of the underlying security. Delta is expressed in cents, showing how many cents an option will rise or fall given a \$1 move in the stock.

Delta is positive for calls and negative for puts. This makes sense because calls gain value when stocks rise and puts gain value to the downside. Having negative deltas mean that puts move in the opposite direction as the stock.

To illustrate, imagine a stock is at \$20. Say one of its calls costs \$1 and has 0.50 delta.

If the stock climbs \$1 to \$21, the call could appreciate by \$0.50 to \$1.50. If the shares fall \$1 to \$19, the calls will depreciate by about \$0.50 to \$0.50.

This highlights the potential leverage in options because a 5 percent move in the stock (from \$20 to \$21) can boost the calls by 50 percent. Likewise a 5 percent drop can cut their value roughly in half.

Using puts, imagine the same stock is at \$20. Say one of its puts costs \$1 and has -0.50 delta.

If the shares decline from \$20 to \$19, the puts could appreciate by \$0.50 to \$1.50. If the stock rises \$1 to \$21, the puts will depreciate by about \$0.50 to \$0.50.

Because delta tracks direction, our memory trick is “Delta: D is for direction.”

## Gamma

Gamma shows how much delta an option gains or loses when the underlying stock moves.

In the example above, we say that the call or put gains or loses “about” \$0.50 because the delta changes slightly as the stock rises or falls. Gamma explains this change.

If the calls have gamma of 0.10, their delta will increase by 0.1 as the stock rises by \$1. That could mean the calls will appreciate roughly \$0.55 instead of \$0.50. (Remember that the 0.60 delta would only be effective at the end of the move, which explains why they don’t gain by \$0.60.)

The same thing applies to the puts, but in the opposite direction. If their gamma is 0.10, the delta will change from -0.5 to -0.60 as the stock drops from \$20 to \$19. Therefore they could appreciate by about \$0.55.

From these examples, we see that options can track underlying stock more closely as its price moves in the intended direction. Calls often have more delta as stocks rally and puts can increase their correlation to the downside. When prices move sufficiently into the money, the calls will have a delta of 1 and the puts will have a delta of -1. That means they can track the underlying on a dollar-for-dollar basis.

In other words, delta can increase when prices move in favor of the option. This can potentially boost profits when traders correctly identify the direction of a stock. (If they’re wrong, their position could quickly lose value and expire worthless.)

If delta describes leverage, gamma can be considered “leverage on leverage” because it describes how delta changes based on movements in the underlying security.

Given this dynamic, our memory trick is “Gamma: G is for gaining delta.”

## Theta

Theta shows how much value an option loses each day based on time decay. It’s always a negative number, expressed outright in cents.

A call or put with -0.20 theta will lose an estimated \$0.20 per day (assuming the stock doesn’t move and implied volatility doesn’t change).

Options with more time until expiration have more time value. This reflects the fact that more things — good or bad — can potentially happen and impact the underlying stock price. Likewise, options with little time have less potential for unknown factors to arise.

Time value initially declines at a relatively smooth pace if expiration is several months or years away. It accelerates as expiration approaches, which is reflected in greater theta for shorter-dated calls and puts. (The numbers are bigger in absolute terms because they’re negative.)

Interestingly, theta can be the mirror image of gamma. Shorter-dated options have more gamma (price leverage) but lose time much faster. This is another way of understanding risk and reward. Everything has a price. In this case, the price of leverage is faster time decay.

Our memory trick is “Theta: T is for time decay.”

## Vega

Vega shows how implied volatility impacts the price of options. Simply put, stocks with the potential for violent moves tend to have more expensive calls and puts. (This might be evident with an industry like biotechnology.) The opposite can be true for slow-moving sectors like consumer staples.

Volatility estimates annualized moves, or how much a stock could move over the course of a year. Historical volatility shows annualized moves based on recent history (like 10 or 20 sessions.) Implied volatility estimates the potential for future movement.

Not surprisingly, implied volatility tends to be higher for stocks with higher historical volatility. This explains why fast-moving stocks have more expensive calls and puts.

Nonetheless, implied volatility can change. It might increase if the broader market is swinging wildly. It can also increase before major events like earnings.

Vega shows how much an option’s value will change if implied volatility moves by 1 percentage point. An option with 0.5 vega will gain \$0.50 if implied volatility increases by 1 percentage point. It will decline about \$0.50 if implied volatility drops by 1 percentage point.

Vega is higher for options with more time until expiration. This isn’t a surprise because they have more time to be be impacted by events.

Our memory trick is “Vega: V is for volatility.”

In conclusion, options are fast-moving, complex instruments. They often seem complicated because they’re derivatives with complex pricing models. However, traders can understand the basics of how Greeks impact their value. Hopefully the four memory tricks cited above helps you keep track of these key nuances.

To recap:

• Delta: D is for direction
• Gamma: G is for gaining delta
• Theta: T is for time decay
• Vega: V is for volatility

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