# Guide to Option Greeks

**Aristides Georgacopoulos**

The sensitivity of an option to the various underlying factors which determine its price is measured by risk parameters commonly known as "the Greeks". These are labelled as such because they predominantly take their names from letters of the Greek alphabet.

Although some of these risk parameters can get quite complex, the vast majority of options traders only need to grasp the concepts of the most important Greeks: Delta, Gamma, Vega, Theta, and Rho.

## Delta

Delta measures the sensitivity of an option to a shift in the underlying asset, essentially describing how much the price of the former will change for a given move in the price of the latter.

Call options have positive deltas, reflecting the fact that their price increases with an increase in the price of the underlying asset, all other things being equal. Correspondingly, puts have negative deltas. In absolute terms, the delta of an option is a number that's bound between 0 and 1 (or 0 and 100 when expressed in percentage terms), with that of at-the-money options being close to 0.5.

Delta is also commonly regarded as an indication of the probability, at any given point in time, that the option will expire in the money.

## Gamma

Delta is only useful in determining an option's sensitivity to small movements in the underlying, because it doesn't stay constant. The option risk parameter which measures the rate by which delta changes with shifts in the underlying price is called gamma.

Long options have positive gamma, while short options have negative. Gamma is at its highest for at-the-money and close-to-expiry options.

## Vega

Although vega isn't actually a Greek letter, it's one of the most important "Greeks" in options trading; it measures the option's sensitivity to changes in its implied volatility, typically for a move of 1% in the latter.

As with gamma, long options have positive vega, while short options have negative. Contrary to the case for gamma, though, the more time there remains until the option's expiry, the greater its vega will be. Vega is thus one of the important risk considerations for longer-dated options.

## Theta

Theta is the risk parameter used to describe the time decay in the option's value. It's typically expressed as the loss the option will suffer for one calendar day. For that reason, options are often quoted lower on Fridays, in order to incorporate the effects of three days' worth of time value about to be lost.

Theta can be thought of as a trade-off for gamma. Long options have negative theta, and short options have positive.

## Rho

Rho is generally considered the least important of the most commonly followed Greeks. It describes an option's sensitivity to changes in the interest rate used to derive the option's value.

An increase in interest rates will increase the underlying's forward price, and will therefore be good for call options and bad for puts. The former therefore have positive rho, while the latter negative.

## Conclusion

A good grasp of the most important Greeks is a pre-requisite for trading options successfully. Taken together, they provide an all-around view of an option's potential risks and rewards. Moreover, in conjunction with the option's implied volatility, they can also serve as a measure of an option's value and how that is likely to evolve in the future.