Options Premium and the Greeks

Futures contracts can be an effective and efficient risk management or trading tool. Their performance is basically two-dimensional, either you are up money or down depending on the entry price point and whether the market is up or down versus your position.

But with options on futures there are more dimensions, or forces, acting on the price, or premium, of the option.

There are metrics to measure each of these different forces impacts on the premium of an options. These metrics are often referred to by their Greek letter and collectively as the Greeks.

While we have addressed each Greek separately, it is important to understand they do not operate independently, but move and adjust dynamically with changes in market conditions. 

Assume futures are at 980. The 1000 call is priced at 12 with a:

Delta of 40

Gamma of 0.50

Theta equal to 0.20

Vega equal to 0.10 and

Volatility at 15%

If market goes to 1000 (up 20 points) in 2 weeks  and volatility drops to 14% (down one point) what is the resulting premium of the option?

Look at each one of our Greeks.

The effect on the option’s premium from delta alone would be .40  x 20 which equals 8 points.

To calculate the delta effect due to gamma, we multiply the gamma of .50 times the 20-point move, giving us 10 additional delta. This changes the options delta from 40 to 50.

The initial delta is 40, which would generate 8 points of change across the 20-point move. The new delta of 50 would generate a premium change of 10. Across the 20-point move, the delta changed from 40 to 50, therefore we take the average, 45. This will contribute 9 points to the options new premium.

To calculate theta, or time decay, multiply the theta value of 0.20 times 14 days which equals -2.8

The vega effect is calculated by multiplying the vega metric by the change in volatility.

Vega of -1 x 0.10 = -0.1

Now we can add those values to get our new option price.

Old option premium + delta + theta + volatility

The option premium is now 18.1

You should now have a greater understanding of how the options Greeks work together. Recognizing the pricing variables of options is a necessary component of option trading.