# How is Probability of Profit Calculated?

The Skinny On Options Math

Options involve risk and are not suitable for all investors. Please read Characteristics and Risks of Standardized Options before deciding to invest in options.

A crucial metric here at tastytrade, probability of profit (POP) gives us a gauge of potential success on different trades. We get a lot of questions about this, and so we wanted to clarify its calculations, both formally and ‘back of the envelope’ style.

Jacob, a grad student at the University of Chicago and our resident mathematician joins the show to cover these formulas.

First, he outlines some basics about calculating probability of profit. Jacob emphasizes that the formal calculation is dependent on the model that is used to assess the probabilities of the underlying’s movement. We must also understand where the break-evens are on a trade to calculate probability of profit, which can be calculated if we know the credit/debit earned on a trade.

When formally calculating the POP, an assumption must be made about the distribution of the underlying’s movement. Options pricing models are used to accomplish this, with Black Scholes being perhaps the simplest and most widely used. This allows us to model the probabilities of an underlying getting to certain ranges.

Jacob reviews the Black Scholes formula, pointing out where inputs like the strike price, credit received, risk free rate, time, and volatility come in. From this formula, the probability of profit can be derived. However, Jacob discusses some additional things to keep in mind when interpreting the final statistic, including the assumption that the trade will be held until expiration.

To reach a calculation quicker, a ‘back of the envelope calculation’ may be more useful. Jacob provides a simplified rough calculation, which only requires the max profit and max loss as inputs.

This calculation differs from the probability of expiring below a breakeven because it does not take into account that trades can be managed at less than max profit or loss. Finally, Jacob explains how the calculation’s accuracy is affected for narrower and wider defined risk spreads, and that it is minimally affected by directional or systemic bias.

In summation, probability of profit calculations, whether they are done formally though the dough platform or informally on a napkin, can give us a better sense of possible success rates on a trade.