Black-Scholes Model: Why Option Perks Uses Historical Volatility to Calculate EV

To conclude our conversation on raw expected values, I’d like to come full circle and discuss the equation that makes all this possible: Black-Scholes.

We’ll explore how this one formula allows us to calculate probabilities and expected values in multiple ways. We’ll compare the different methods to show you why Option Alpha chooses to use the annualized 30-day standard deviation of returns as the volatility input to Black-Scholes.

If you’re just joining us, I highly recommend starting with our first two articles in this series: Trade Ideas Probability and Performance and How to Calculate Expected Value.

Brief Review of the Black-Scholes-Merton Model

The Black-Scholes-Merton (BSM) model is a seminal work in financial mathematics, providing a theoretical framework for pricing European-style options. Developed independently by Fischer Black, Myron Scholes, and Robert Merton, the model is predicated on a set of assumptions, including: 

• The absence of transaction costs and taxes.
• Constant risk-free interest rate and volatility.
• Log-normally distributed returns.
• The ability to short-sell and purchase fractional shares.