Options questions come up most at firms that make markets in options, such as Optiver, SIG, IMC and Akuna. They rarely ask for a derivation. They ask what a position is worth, what it gains or loses when the stock, volatility or time moves, and whether a set of quoted prices leaves an arbitrage.

1. 1

   Put-call parity

   A call minus a put on the same strike and expiry equals the stock minus the discounted strike. Any quote that breaks it is an arbitrage, and many questions are this one identity in disguise.

2. 2

   Delta and gamma

   An at-the-money call has a delta near 0.5. Gamma, the rate delta changes, is largest at the money and grows as expiry approaches.

3. 3

   The at-the-money rule of thumb

   An at-the-money call is worth about 0.4 times volatility times the square root of time times the stock price, which turns a quote into an implied volatility in your head.

4. 4

   Delta-hedged P&L

   A delta-hedged long option makes money when the stock moves more than its implied volatility priced in, and loses time value when it moves less.