# How to compute delta and delta-hedge in practice?

I keep hearing things like \begin{align*} \text{Traders make their book delta-neutral at the end of each trading day''} \end{align*} I am wondering what this means, and why this is supposed to give the traders some peace of mind.

More specifically: How do the traders compute delta and decide how to hedge an option position? Do they assume the Black-Scholes model (or some other model) and then compute delta? In that case, what about model error (delta is the partial derivative w.r.t. price and is model-specific)? Thus, the delta they compute may be completely wrong!

Similarly, I have some market data from a financial data vendor, containing S&500 call and put option prices, as well as the delta, gamma, etc. of the options. In general situations like that, how are those quantities computed? Is it simply under Black-Scholes assumptions?