Probability of profit

Level 3 - Options Wizards Only

There is a lot of material on the Internet and books that talk about option payoffs. But very few really talk about the probability of achieving those payoffs. In this section, we will attempt to understand how to evaluate this aspect to hopefully give the readers a chance to sharpen their trading edge.

We know that:

Expected profit = Summation of [probability of profit* Payoff ]

Before we head into calculating probability of profit of an option, let’s quickly delve into understanding cumulative distribution function (cdf)

A CDF is a tool used in statistics to show the probability that a random variable will take on a value less than or equal to a certain amount. In simpler terms, it tells us how likely it is that something will happen up to a certain point.

When we use the market’s option prices to back-calculate this CDF, we are looking at the Risk-Neutral Probability. It’s not necessarily a "prediction" of the future, but a map of what the market is currently charging for those outcomes.

For instance, following is the cdf of a dice roll.