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# How does a delta signify the probability of expiring in the money

2018-10-19 05:01:36

I was watching this video on option greeks

and the guy said (at 34 min): If an option has a delta of 34, it has a 34% probability of expiring in the money? Is it possible to understand it intuitively without getting into the math of Black Scholes formula?

Just for clarification, delta and probability of expiring in the money are not the same thing. What the guy meant was that delta is usually a close enough approximation to the probability.

One way to think about it is to look at the probabilities and deltas of In the Money, Out of the Money, and At the Money options.

A deep in the money option has a really high chance of expiring in the money, around 100%, and it has about 100 delta

A far out of the money option has a really low chance of expiring in the money, around 0%, and it has about 0 delta

An at the money option has about 50% probability of being in the money because there is a 50-50 chance the stock will go up or down, and it has about 50 delta

In th

• Just for clarification, delta and probability of expiring in the money are not the same thing. What the guy meant was that delta is usually a close enough approximation to the probability.

One way to think about it is to look at the probabilities and deltas of In the Money, Out of the Money, and At the Money options.

A deep in the money option has a really high chance of expiring in the money, around 100%, and it has about 100 delta

A far out of the money option has a really low chance of expiring in the money, around 0%, and it has about 0 delta

An at the money option has about 50% probability of being in the money because there is a 50-50 chance the stock will go up or down, and it has about 50 delta

In these cases, the delta and probabilities are about the same. In fact if you look at an options chain with delta and probabilities, you can see that they are all about the same. In other words, there is a linear relationship between delta and probability.

Here are a couple lin

2018-10-19 05:40:43