## Greeks

Greeks play an important role in risk management and specifically in option valuation. Greeks determine the sensitivity of an option to a change in underlying variables, meaning the effect a change in a variable will have on the value of an option. There are a number of different variables which can influence the value of an option, with many common variables being represented by Greek letters. These change variables range from the price of the underlying asset, volatility rate, interest rate to the time until expiration. All these variables can change the value of an option, where some variables may have a more significant effect on the value than other variables. It is important to understand these factors, to be able to calculate their impact on an option’s value and consequently implement hedges against these possible price fluctuations.

#### Delta (Δ)

The Delta of an option determines the effect a change in the underlying asset will have on the option itself. A Delta for calls will range from 0 to 1 and for puts from 0 to -1. Where for example a Delta of 0.4 on a call option will give an increase of $ 0.40, when the price of the underlying assets rises with $ 1. The time until expiration will also influence the Delta. Where the experation date comes closer the Delta will likely reach its maximum Delta, because a change in the underlying price will have a more lasting effect on the option.

A Delta can also be used to determine the probability of an option expiring in the money and thus generating a profit. For example an option with a Delta 0f 0.4 gives traders an indication there is a 40 percent chance the option will expire in the money and thus generate a profit upon exercising the option.

#### Vega (ϒ)

The Vega of an option determines the impact a 1 percent change of the underlying volatility will have on the value of an option. In many markets the price of an option will increase along with increasing volatility. As an option in a highly volatile market has a bigger chance of generating a great profit the price for this option will also be higher. When the volatility increases the Vega is added to the price of an option and subtracted when the volatility decreases.

#### Theta (Θ)

The Theta of an option describes the impact, a nearing experation date, will have on an option. When the expiration date of an option draws near the option will lose value, because the opportunities to take advantage of price fluctuations becomes limited. Therefore the Theta generally is a negative number. With longer term options the Theta value is usually very low and starts to increase significantly with the experation date drawing near.

#### Gamma (Γ)

Gamma is used to describe the change in the Delta of an option, when the price of the underlying asset changes. Meaning it is a second-order indicator of the impact changes in the price of the underlying assets, have on the value of an option. A gamma is important factor because it tells traders how much of an impact the next price change of the underlying asset will have on the value of an option. For example a Gamma of 0.1 means that the Delta will increase with this percentage. Thus if the Delta was 0.3 percent with a recent price change of 1 percent, the next price change of 1 percent will result in a Delta of 0.4 percent. The Gamma is added to the Delta and thus gives an indication of the curvature of the price curve.

#### Rho (ρ)

Rho is an indicator for the impact interest rates have on the value of an option. This is the Greek with the least impact on the value of an option. Because interest rates usually don’t change dramatically, the impact on the value of an option is quite insignificant. Furthermore the other Greeks have a more significant impact on the value which makes the impact of Rho almost negligible, unless all the other Greeks remain stagnant, which virtually never occurs.