# The Greeks

**THE GREEKS**

Several different factors combined determine the value of an options contract. The price of the underlying instrument is the most influential, but that’s not the only determinant of an options premium. The time left to expiration and the volatility of the underlying instrument can also have a significant impact on prices. The so-called “Greeks” are quantitative measures that help to gauge how much the contract is expected to change based on changes in the underlying price, the volatility and time. The values are computed using an options-pricing model, but are also available in the options quote lists and chains. Knowing them isn’t essential to trading options, but a basic understanding of the concepts should not be overlooked.

DELTA

Even novice options traders understand that the value of an options contract increases and decreases with the price of the underlying security (stock, index, futures, etc). If, for example, I buy an Apple September 800 call, I want Apple to move higher in price and for the call to increase in price. On the other hand, if I buy a Micosoft May 25 put, I want Microsoft shares to fall and for the put to increase in value. However, options do not necessarily move point-for-point with the underlying stock.

Delta measures the amount a put or call option contract is expected to change for every one-point move in the forex. Delta can range from -1.0 to 1.0. For instance, if you want to know how much a call will increase in value if the stock moves higher, you can get a general idea by looking at the option’s delta. A call with a .20 delta increases in value by 20 cents for every one-point increase in the underlying stock. It will lose 20 cents if the pair declines by 1-point. Put options have negative deltas that range from -1.0 to 0 because the contract will lose value as the stock rises and increase in value it falls. The underlying security has a delta of 1.0 and calls have deltas ranging from 0 to 1.0.

There is an important relationship between moneyness and the delta of an option. A call option is in-the-money [ITM] when the underlying price is trading above the strike price of the options contract and is out-of-the-money [OTM] when the stock price is below the strike. As a general rule, ITM options are more responsive to changes in the underlying and have higher deltas than OTM options. At-the-money [ATM] call options, where the strike price equals the stock prices, have deltas near .50. At-the-money puts have deltas of -.50. There is a 50/50 shot they will be in-the-money at expiration. Delta also measures the probability that an option will be in-the-money at expiration.

The time left until expiration is another factor that will determine how much delta is in an option. The delta of an ITM option will approach 1 as expiration approaches, which means it will move almost point-for-point with the underlying. Since there is very little time value left near the expiration, the contract will be very responsive to changes in price of the underlying. The contract has a high delta. On the flip side, however, delta of an OTM option contract will approach zero near the expiration. So, near expiration, the delta of a contract can quickly change if the contract moves from in-the-money to out-of-the-money.

GAMMA

Gamma measures how much delta is expected to change for each point move in the underlying. For example, a contract that has a gamma of .10 will experience a .10 increase in delta for every point move higher in the underlying. Long options, whether puts or calls, have positive gamma and short options have negative gamma. Short-term at-the-money contracts have the highest gammas, which diminishes as you go up or down the strikes and or to more distant expiration months. For example, a contract that quickly moves to in-the-money from out-of-the-money near expiration will see delta rapidly increase. Gamma is quite high. However, a long-dated out-of-the-money will see relatively slow changes in delta. It has low gamma.

VEGA

Vega is not actually a Greek letter, but it is considered one of the Greeks when dealing with options prices. It measures the amount an options contract is expected to change for each point change in implied volatility, which is the amount of volatility priced into the options premium and also computed using an options pricing model. For example, the EUR/USD June 1.30 call might have implied volatility of 12 percent and vega of .10. If so, the premium will increase by 10 cents for every 1-point increase in implied volatility. Long options have positive vega and short options have negative vega. Vega is typically higher in the at-the-money long-dated options and decreases up and down the strikes and or in the nearer-term expirations.

THETA

Time decay affects all options and Theta measures how much a contract will lose with each passing day. A theta of .05 indicates the contract will loses 5 cents in one day. Long options have negative theta and short options have positive theta. In addition, time decay is not linear and affects short-term options more than longer-term ones. In other words, short-term options will have higher theta relative to longer-term ones.

Seasoned options traders rely on the Greeks to measure how much premiums are expected to change due to time decay, changes in implied volatility, and moves in the underlying asset. The Greeks are also important when creating more advanced strategies, hedging, and trading volatility. For example, if the investor holds a position in Facebook shares the delta of that position is 1.0. To hedge the position, one would need to buy a put with a delta of -1.0, two puts with a delta of -.50 or maybe three puts with -.33 delta. Or, before opening a calendar spread, the investor might check theta to see how time decay will impact the short-term option relative to the longer-term one. Both theta and vega are important when creating volatility plays like straddles and strangles. While not all options traders use the Greeks, it makes sense to understand what they represent and how each give an indication on how or why options prices are changing from one day to the next.