Question

10. Interpret the following option greeks’ values for a call option:

Delta Gamma Theta Vega Rho

0.819 0.00205 -0.397 0.963 0.945

Answer 1

DELTA

Delta is the amount an option price is expected to move based on a $1 change in the underlying stock.

Calls have positive delta, between 0 and 1. That means if the stock price goes up and no other pricing variables change, the price for the call will go up. Here’s an example. If a call has a delta of .50 and the stock goes up by $1, in theory, the price of the call will go up about $.50. If the stock goes down $1, in theory, the price of the call will go down about $.50.

Hence in our question, a call has a delta of .819 and the stock goes up by $1, in theory, the price of the call will go up about $.819. If the stock goes down $1, in theory, the price of the call will go down about $.819.

As a general rule, in-the-money options will move more than out-of-the-money options, and short-term options will react more than longer-term options to the same price change in the stock.

GAMMA

Gamma is the rate that delta will change based on a $1 change in the stock price. So if delta is the “speed” at which option prices change, you can think of gamma as the “acceleration.” Options with the highest gamma are the most responsive to changes in the price of the underlying stock.

Understand this using the below table showing changes in stock price, delta & thus showing gamma-

	Stock at $48	Stock at $49
DELTA	0.819	0.82105
GAMMA	0.00205

THETA

Time decay, or theta, is enemy number one for the option buyer. On the other hand, it’s usually the option seller’s best friend. Theta is the amount the price of calls and puts will decrease (at least in theory) for a one-day change in the time to expiration.

Check out the figure, As you can see, an at-the-money 90-day option with a premium of $1.70 will lose $.30 of its value in one month. A 60-day option, on the other hand, might lose $.40 of its value over the course of the following month. And the 30-day option will lose the entire remaining $1 of time value by expiration.

In our case, in a day's movement, the price of option premium will reduce by 0.397.

VEGA

Vega is the amount call and put prices will change, in theory, for a corresponding one-point change in implied volatility. Vega does not have any effect on the intrinsic value of options; it only affects the “time value” of an option’s price.

Let’s examine a 30-day option on stock XYZ with a $50 strike price and the stock exactly at $50. Vega for this option might be .03. In other words, the value of the option might go up by $.03 if implied volatility increases one point, and the value of the option might go down $.03 if implied volatility decreases one point.

In our case, for a 30-day option on stock XYZ with a $50 strike price and the stock exactly at $50. Vega for this option will be .963. In other words, the value of the option might go up by $.963 if implied volatility increases one point, and the value of the option might go down $.963 if implied volatility decreases one point.

RHO

Rho is the rate at which the price of an option changes relative to a change in the risk-free rate of interest. Rho measures the sensitivity of an option or options portfolio to a change in interest rate.

For example, if an option or options portfolio has a rho of 1.0, then for every 1 percentage-point increase in interest rates, the value of the option (or portfolio) increases by 1 percent.

In our case, Rho is 0.945, thus for every 1% increase in interest rates, value of call option will increase by 0.945.