How to use Delta and Gamma when Trading Options

In the world of options, delta is the theoretical equity value of the underlying shares of a stock of that particular option. Delta can be either positive or negative. If a delta is positive, that delta represents long stock. If that delta is negative, that delta represents short stock. The total value of the delta of any particular option is a dynamic number, changing throughout its contractual life as the price of the underlying stock changes in price. A delta of 100 represents the theoretical equivalent to that of 100 long shares of the underlying stock. A delta of -100 represents the theoretical equivalent to that of 100 short shares of the underlying stock.

Any option that is “deep in-the-money” is an option that is monetarily equivalent to being worth 100 shares long or short of the underlying stock. Any delta of +100 or -100 would imply a deep in-the-money call or put, the plus delta being long and the minus delta being short. A delta of +50 or -50 would imply a call or put which is known as being “at-the-money”. For example, a stock that is trading at 30 would have both a 30 strike call and a 30 strike put listed on the various options exchanges. The call and the put would be considered at-the-money as well as having a delta of +50 if a call or -50 if a put.

As the underlying stock moves up or down, the delta of that 30 strike call or put would also gain or lose delta. Assume that the stock went up to 31 during that day. The 30 strike call with a delta of +50 when the stock was trading at 30 would have its delta Increase to approximately +60 when the stock began trading at 31. The 30 strike put would see its delta move down in value with the stock moving up to 31. The delta of that put would be -40 at that point. The mathematical reason that the put delta would drop to -40 is that the combination of the call and put must equal 100 at all times, given that the strike price and the expiration series are equivalent. Should the stock have declined to 29, the put delta would Increase to approximately -60 and the call delta would decline to +40. Once again, when adding up the delta values of the corresponding put and call, the total would be 100 deltas.

Gamma is the rate of change of the delta for any 1 point move in the underlying stock in either direction. Gamma is the “gas pedal” for delta. The more gamma you have, the faster your delta will change. The more gamma you have, the quicker your delta moves as the underlying stock moves. Gamma is either positive gamma or negative gamma. If you have positive gamma, then as the underlying stock declines in price, you will see the negative delta total grow More negative. Thus the position of the options grows to being more short the underlying stock.

If you have positive gamma, then as the underlying stock rises in price, you will see the positive delta total grow More positive. If you have negative gamma, then as the underlying stock declines in price, you will see that the negative delta total declines from being negative, moving in the positive direction. If you have negative gamma, then as the underlying stock increases in price, you will see that the positive delta total declines from being positive, moving in the negative direction.

Positive gamma allows for the total of the options positions of that particular stock to correspondingly move in delta value as the direction of that the underlying stock changes in price. Positive gamma by its title and nature implies that you are long more options (both puts and calls) than you are short options on that particular stock. Negative gamma allows for the total of the options positions of that particular stock to inversely move in delta value as the direction of that underlying stock changes in price. Negative gamma by its title and nature implies that you are short more options (both puts and calls) than you are long options on that particular stock.

A working knowledge of how delta and gamma are used in the options trading world can only enhance the sophistication of any stock and options markets participant. Should you chose to get involved in building an options position in any particular stock, working with a professional options brokerage firm is highly recommended. These firms understand the intricacies of the options world far beyond delta and gamma. Most brokerage firms do not have the expertise to help you manage any options portfolio, so it is best to avoid them when trading options.