In day-to-day trading on a real options desk, how often does someone actually compute the BSM formula by hand?

Almost never by hand. But you will read BSM-derived numbers off a screen approximately 2,000 times per day, so the formula is still load-bearing.

The realistic workflow:

1. Pricing. The trader sees mid-market and bid-ask. The pricing engine — usually a proprietary C++/CUDA system, sometimes Bloomberg DLIB, sometimes Murex — runs the BSM formula in microseconds, but with the implied volatility surface as an input (not a single constant vol).
2. Risk reporting. The end-of-day risk file lists net delta, net gamma, net vega, net theta, net rho for every book. Every single one of those is a BSM partial derivative aggregated across thousands of positions.
3. Vol marking. Junior quants spend hours each week reconciling the implied-vol surface used by the pricing engine to broker quotes. You will live in BSM coordinates whether you compute the formula yourself or not.

When you DO compute it by hand:

• Sanity-checking a screen quote that looks wrong (back-of-envelope on a calculator)
• Explaining a position to a client or PM who is not an options specialist
• Onboarding into a new product (you compute the formula once, by hand, on a whiteboard with the senior trader watching, so you understand the building blocks)
• Interview screens (yes, banks still ask)

What you should brush up before the internship:

Build that Excel sheet yourself before week one. Your senior trader will hand you a screen with a quoted price and ask, "is that fair?" Knowing how to back-solve implied vol on the spot, in Excel, in under 60 seconds, separates the keepers from the resume-padders.