The Greeks are used to assess risk when buying and selling options. Each of the Greeks considers a particular relationship – rate of change – between the option and some other data point in its assessment:
•Delta = price of option and underlying asset (price sensitivity)
•Theta = option portfolio and time (time sensitivity)
•Gamma = portfolio delta and price of underlying asset (second-order time price sensitivity)
•Vega = portfolio value and underlying asset volatility (volatility sensitivity)
•Rho = portfolio value and interest rate (interest rate sensitivity)
Delta shows the change in the price of a derivative to the change in the price of the underlying assets. Sometimes delta is known as the “hedge ratio,” as delta indicates how much of the underlying asset needs to be bought or sold to hedge the option. Traders take advantage of delta by creating delta hedging, delta spreads, and delta neutral.
Delta values are positive numbers less than or equal to 100. They represent the ratio of the change in the theoretical value over the change in the underlying price.
Values:
Out of the money = close to 0
At the money = close to +0.5
In the money = close to +1
Calls = positive
Puts = negative
Delta values for the out-of-the-money series move closer to 0 as expiration nears. Likewise, more in-the-money options have deltas close to 1 as expiration approaches.
For example: If the underlying S&P 500 contract stands at 134020, with a delta of 52.73, and a theoretical value of 2600.5, and the underlying price increases to 134220, while the delta rises to 54.02, the theoretical value increases to 2707.
The calculations are:
134220 – 134020 = 200
(52.73 + 54.02)/2 = 106.750
53.375 *2 = 106.750
The deltas from one underlying price to the next are interpolated.
106.750 + 2600.5 = 2707.25 new theoretical value
Theta represents the loss in theoretical value in one day, if all other factors are constant. In other words, it attempts to isolate the time decay factor.
For example: Assume the amount showing the Value column was 2725.1, with 15 days until expiration and a theta value of 92.053. You would expect to see the amount in the Value column decrease approximately 92 dollars the following day. A more precise definition of the amount of the time value lost is an average of the thetas on the dates under consideration. So, if the theta on the following day was 95.201, the decrease in theoretical value would be:
(92.053 + 95.201)/2 = 93.6
Gamma is the amount the delta changes when the underlying price changes by one tick.
Gamma is greatest for at-the-money options. Gamma increases as the option moves closer to expiration. Traders try to limit gamma risk because short gamma positions create a potential for losses.
For example: If the delta of an S&P future was 91.80, the gamma was .01 and the price of an S&P future increased from 1340.80 to 1340.90 i.e., a one-tick increase, the delta would increase to 91.81.
Vega
Vega is the amount that the theoretical value changes when the volatility changes by 1 point.
For example: Assume a June Corn contract had a vega of 1.421, a volatility of 25.90, and a theoretical value of 45.4. If the volatility were to increase to 26.90, the vega says that the theoretical value would increase by 1.4 dollars to 46.8, provided the other factors affecting options prices remained constant.
The display also indicates the days until expiration, as well as the volatility and interest rate assumptions underlying the data.
Rho
Rho is the change in option price to a unit change in interest rates. When the interest rate increases, the call option price increases also and put option price falls.
For example: Assume the starting call value is 4.2012, the interest rate r is 5% and zero-coupon rate b is 2%. Rho(r)(per 1%)= 0.1243, and Rho(b)(per 1%)=0.1328, If r rises to 6% and b stays at 5%, the call value is 4.3255. If r stays at 5% and b rises to 3%, the call value is 4.334.