# How do I find the probability of a sold put being assigned?

I read where if you sell a put you should make sure that the probability of being put the stock is no more than 30%. This is assuming of course that you don't really want to own the stock. How do I find what the probability is? Is there a greek symbol or something for that?

The Delta of an option is a rough estimate of the probability of an option expiring in-the-money (and hence getting assigned). An at-the-money option with a delta of about 0.5 has roughly a 50% change of expiring in the money (the underlying price could go either way), a deep-in-the-money option with a delta approaching 1 will almost assuredly pay out, and a deep out-of-the-money option with a delta approaching zero has almost no change of paying out.

In reality, delta is always slightly larger than the probability of exercise, and the difference is greater for highly volatile underlyings and longer-dated options, but the relationship still holds, and since you're using a rule-of-thumb (30%) anyways, should be "good enough" for your rule.

To a first order approximation, the probability is very near to delta, as mentioned already.

Additionally, if you look at an options chain, usually most websites and brokers offer an alternative column with ITM likelihood (not to be confused with a Probability of Profit metric, which incorporates the premium of the option at time of sale). They deviate by less than 5% under normal circumstances. Delta is larger because it not only factors the binomial likelihood of ITM, but it's also dependent on the degree by which the option expires with intrinsic value.

I'm not sure exactly how this is calculated or interpolated other than the fact that there are tables with rounded values that already exist, but it derives from B-S-M when computing N(d2), which amounts to estimating a normal CDF. A Taylor approximation may be used to calculate the estimate, perhaps? This is all, of course, the case of European options, and American options are different because holders can exercise early.

Note that delta is N(d1) for calls and N(d1) - 1 for puts where

For reference, see The Pricing of Options and Corporate Liabilities (1973): https://www.cs.princeton.edu/courses/archive/fall09/cos323/papers/black_scholes73.pdf

This is also explored in Hull 9th, for example on pg 338.