Options Greeks and Options Risk Management

What is the Delta of an option?

The Delta is a measure of how much the value of the option moves when the price of the underlying moves. If the underlying price moves up, the Delta tells you how quickly the value of the option moves with it. 

Assume the price of the underlying moves up by $1 and the value of the option increases by $0.25, the Delta is 0.25. 

Delta is often used as a proxy for the probability that an option will be exercised, this is due to the fact that in the money options generally have a Delta greater than 50%. 

What is the Gamma of an option? 

Gamma is the rate of change of an options Delta compared to the underlying asset’s price. Higher Gamma indicates that the Delta could change significantly, even with small price changes in the underlying. 

Being long Gamma is a good thing. A call option gives a long Delta position and as the market rises it gets longer. You pay for Gamma when you pay a premium for the option. 

What is the Theta of an option? 

Theta is less of a risk measure and more of a measure of exposure to the passage of time. As each day passes, the option loses value. This decay in option values over time is sometimes referred to by options traders as the “rent” that is paid to be long gamma.

If a call option with 3 months to expiration is worth 10.42, and with 2 months to expiration it is worth 7.36, it has dropped 3.06 over the month, or $36.70 per year, which is Theta. 

What is the Vega of an option? 

The Vega of an option indicates what happens to the value of an option when the volatility of the underlying changes. 

If a 3 month option with 10% volatility was priced at 10.42, and at 11% volatility the price moved up to 12.08, the Vega is 1.67 per vol point.