Option Trading Blog

This is the continuation of the series about what is known as the “greeks”. In this post, I’ll talk about the Gamma of an option. Read about the delta here .For those who are wondering where all of this is leading if at all, I’m planning later on writing more methods rarely discussed, but those require knowing a bit of background. So be patient.

If you recall, the delta of out-of-the-money options is close to zero, while the deep-in-the-money delta is close to 100. A question that can be asked at this moment is, how does the delta of a call option itself change as the price of the stock changes? We can expect that as the stock price falls, the delta rises close to 100, and vice versa, when the stock price rises, the delta gets close to zero. We can also expect that the delta of a put option rises as the stock price declines and vice versa.

The gamma of an option, is the rate at which an option’s delta changes as the price of the underlying changes. For instance, if an option has a gamma of 10, for each point rise in the stock, the delta rises by 10 and vice versa. This means that if the option had a delta of 50, and the stock has risen by one point, the delta would now be 60.

Important note: Unlike delta, the gamma for both put and call options is positive. Suppose we have a call option with a delta of 30 and a put with a delta of -40, both with a gamma of 5. When the stock rises by one point, the delta of the call option would be 35 and of the put -35. This is actually intuitive as we would have expected. At-the-money calls get into-the-money while into-the-money puts move out-of-the-money.The gamma has an important role of determining risks. If the gamma is very big, the option can change it’s price rapidly.

An example: Consider a trader who sells ten calls with a delta of 50 each. He is short 500 deltas (-500). This is equivalent to shorting 5 stocks (). What happens if the stock rises by 5 points? If he is short the 5 stocks, he is still short 500 deltas (ignore the fact he may have lost money). But what happens to the delta if he had the short portfolio of 10 calls? Assuming the call option had a gamma of 5, his portfolio’s delta is

Big gamma positions can be very tricky and dangerous. Especially negative ones. If a trader has is short on a very big gamma position, a sudden upward move can be disastrous.