Option Greeks explained for trading interviews

The Greeks describe how an option's price changes when one input changes. Interviewers use them to see whether you understand options or have only memorised payoffs.

Delta

How much the option price moves when the stock moves by 1.

• Calls have a delta between 0 and 1, puts between −1 and 0.
• An at-the-money option has a delta of about 0.5 (−0.5 for a put).
• For the same strike and expiry, put delta = call delta − 1.
• Delta is also the hedge ratio: long 10 calls with a delta of 0.4 on 100 shares each is hedged by shorting 400 shares.

Gamma

How much delta changes when the stock moves by 1.

• Long options, calls and puts alike, have positive gamma.
• Gamma is highest at the money and close to expiry.
• Long gamma is pleasant to hedge: after a rally your delta is positive so you sell, after a fall you buy. You sell high and buy low.

Theta

What the option loses per day if nothing else moves.

Theta is the price of gamma. A long option position earns from movement and pays for it in time decay. If the stock moves more than the option price implied, the holder wins. If it moves less, the seller wins.

Vega

How much the price changes for a one-point change in implied volatility.

• All long options have positive vega.
• Vega is largest at the money and grows with time to expiry.
• A long-dated option is mainly a volatility position. A short-dated one is mainly a gamma position.

Rho

Sensitivity to interest rates. Higher rates help calls and hurt puts, because they raise the forward price. It matters least for short-dated options.

Rules of thumb worth knowing

• Rule of 16. Annual volatility divided by 16 is roughly the daily move. 32% volatility is about 2% a day.
• At-the-money straddle ≈ 0.8 × stock price × volatility × √time. For a 100 stock, 20% volatility and three months: 0.8 × 100 × 0.2 × 0.5 = 8.
• Put-call parity. Call − put = stock − present value of strike. If it does not hold there is an arbitrage.

Questions you should be able to answer

• Volatility rises. What happens to a call and a put? Both rise.
• You are long a straddle. What are your Greeks? Roughly zero delta, long gamma, long vega, paying theta.
• When does a delta-hedged long option make money? When realised volatility is higher than the implied volatility paid.
• Why is an American call on a non-dividend stock never exercised early? Selling it is always worth at least as much as exercising, because of the remaining time value.
• Which has more gamma: a one-week or a one-year at-the-money option? The one-week option.

Related: how to make a market and the market making game.