What is option delta?
B. Venkatesh
WHAT does the delta measure in an option-pricing model. This article addresses this question.
Delta is the change in the option value for every point change in the stock price.
If the August 210 calls on Satyam has a delta of 53, it means that the calls will change 0.53 point for every point change in the stock price.
If Satyam moves from Rs 210 to Rs 215, the calls will rise by 2.65 points (5 times 0.53).
Another interpretation is that delta can be approximately considered as the probability of the options ending in-the-money.
Thus, in the above example, we can say that there is a 53 per cent probability that the calls will end in-the-money on expiry of the contract.
Unfortunately, delta is only an approximation. Why?
Each time the stock price changes, the option delta also changes.
To make adjustments for this, we use gamma, which measures the change in delta due to the change in stock price.
Suppose gamma for the August 210 Satyam calls is 3, it means that the call delta will change by 0.3 for every 10-point move in the stock price (or 0.03 for every point move). Suppose Satyam moves up Rs 10, the gamma will be 0.3, while the delta will be (10 times 0.53) 5.3. This means that the change in delta is 5.6 (5.3 plus 0.3). We can, therefore, say, that the calls will rise 5.6 points if the stock price moves up by Rs 10.
If the stock falls by Rs 10, however, calls will fall by only 5 points (5.3 minus 0.3).
This is because gamma is always positive, and is added to the delta. |
