TSC Options Forum: Facts About Delta

In descending order, the components that factor into an option's delta are underlying price, strike price, time remaining and interest rates. I recommend using an option calculator such as the one provided at the Chicago Board Options Exchange, plugging in different variables and seeing how they affect delta. For instance, you should note that as a function of time, the delta of in-the-money options increase as expiration approaches, while out-of-the-money options' delta decreases.

An option's delta isn't linear. The rate of change in an option's delta is called its gamma. This is a secondary derivative of the underlying price, and it has little meaning to the nonprofessional trader. For the people who don't deal with options for a living, we need a good method by which we can gauge delta and therefore an option's expected move relative to the underlying security.

You don't need to understand the lift and thrust that propels a plane into flight in order to purchase an airline ticket, but it's still important to know when and where you're going to land. Cleveland on May 3 is very different from Bora Bora on April 28.

To stretch the analogy, a schedule of an option's delta configuration is presented in the table below. These are approximations based on option studies using the strike relative to the underlying stock.

If XYZ stock goes from $30 to $31, we would expect the $30 call to gain 50 cents and the $30 put to drop 50 cents. But again, delta isn't linear, so if XYZ moved to $35 we should expect the call, which is now one strike in the money, to gain roughly $3, or 60%, of the $5 change in the stock. Conversely, the $30 put should lose only $2, or 40%, of the $5 move.

Delta Rule of Thumb Calculation
Option Strike	Estimated Delta
3 strikes in the money	0.85
2 strikes in the money	0.80
1 strike in the money to 2 strikes in the money	0.70
At the money to 1 strike in the money	0.60
At the money	0.50
At the money to 1 strike out of the money	0.40
1 strike out of the money to 2 strikes out of the money	0.30
2 strikes out of the money	0.20
3 strikes out of the money	0.15
Source: Optionetics

Again, these values are predicated on the other elements, such as time and volatility (which while it has no direct bearing on delta does figure into the option's overall price) not changing radically. Remember, an option's delta has little connection to its absolute value or price. That means that two different options, one priced at 50 cents and one priced at $6.50, can both have the same delta.

Next week I'll show how multiple-strike deltas are calculated on a cumulative basis and how to analyze an overall position for hedging purposes.

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