Do I need to memorise the Black–Scholes Greek formulas for interviews?

Rarely. Most trading interviews test qualitative intuition — the signs, what drives each Greek, and the gamma–theta trade-off — not derivations. Knowing the formulas helps, but explaining the intuition cleanly matters more.

What does it mean to be 'long gamma'?

You hold options whose delta rises as the underlying rises and falls as it falls, so a delta-hedged position profits from large moves in either direction. The cost is negative theta: you pay time decay every day you wait for that move.

Why is gamma highest for at-the-money options near expiry?

Near expiry an at-the-money option's delta flips quickly between roughly 0 and 1 as the spot crosses the strike — a small move changes the outcome a lot. That sharp sensitivity of delta to spot is exactly what gamma measures.

The Options Greeks, Explained

An option's price moves for three reasons: the underlying moves, time passes, and volatility changes. The Greeks put a number on each of those sensitivities, and fluent traders think in them the way a driver thinks in speed and acceleration. They are essential at options market makers like Akuna Capital and show up across trading interviews.

The five Greeks at a glance

Greek	Symbol	Sensitivity to	Sign if you are long an option
Delta	Δ	the underlying's price	+ for calls, − for puts
Gamma	Γ	changes in delta	+
Theta	Θ	the passage of time	−
Vega	V	implied volatility	+
Rho	ρ	interest rates	+ for calls, − for puts

Delta, gamma, theta, and vega do almost all the work in practice; rho matters mostly for long-dated options.

Delta: your directional exposure

Delta is the first derivative of the option price $C$ with respect to the underlying $S$ :

$\Delta = \frac{\partial C}{\partial S}.$

A call's delta runs from 0 to 1, and an at-the-money call sits near 0.5. Read it two ways: it is roughly how much the option gains for a one-point move in the underlying, and it is the hedge ratio — to neutralise directional risk you hold $-\Delta$ of the underlying per option. Market makers quote continuously and stay close to delta-neutral so they profit from spread and volatility rather than from guessing direction.

Gamma: how fast delta changes

Gamma is the second derivative — the curvature of the price curve:

$\Gamma = \frac{\partial^2 C}{\partial S^2}.$

It tells you how quickly your delta hedge goes stale as the underlying moves. High gamma means you must re-hedge often.

Key insight. Gamma is largest for at-the-money options near expiry, where a small move in the underlying flips the option between worthless and in-the-money. That knife-edge sensitivity is "pin risk," and it is why near-dated at-the-money options are the most dangerous things to be short.

Theta: the cost of time

Theta measures how much value the option loses as time passes, holding everything else fixed:

$\Theta = \frac{\partial C}{\partial t}.$

Long options have negative theta — they bleed value every day as expiry approaches and less time remains for a favourable move. Sell options instead and theta works for you: you collect that decay.

Vega: exposure to volatility

Vega is sensitivity to implied volatility $\sigma$ :

$\mathcal{V} = \frac{\partial C}{\partial \sigma}.$

Long options have positive vega: they are worth more when the market expects bigger swings. Vega is why an option can lose money even when you called the direction correctly — if implied volatility collapses, the option can fall in value anyway.

The gamma–theta trade-off

Here is the relationship that decides who actually makes money. For a delta-hedged option position, the profit and loss over a short interval is approximately

$\text{PnL} \approx \tfrac{1}{2}\,\Gamma\,(\Delta S)^2 \;+\; \Theta\,\Delta t.$

The first term is your gamma payoff — positive whenever you are long gamma, because $(\Delta S)^2$ is positive whichever way the underlying moves. The second is theta, the rent you pay for holding the option.

The fundamental relationship. Being long options means positive gamma and negative theta; being short flips both. You make money on a delta-hedged long position only when realised volatility exceeds the implied volatility you paid for — gamma is how you harvest the difference, theta is the rent. That one sentence answers a surprising share of options interview questions.

In the interview

You will rarely be asked to derive a Greek. You will be asked to reason:

Worked example. "You are long a call and delta-hedged. How do you make or lose money?" You are long gamma and short theta. As the underlying moves, your delta changes and re-hedging locks in small gains that grow with the square of the move — but you pay theta every day. Net, you profit if the stock realises more volatility than the implied vol baked into the price; otherwise theta wins.

Other staples: "Which has more gamma — a near-expiry or a far-expiry at-the-money option?" (near-expiry), and "Your option gained delta as the stock rose — which Greek is that?" (gamma). For where these sensitivities come from, see Black–Scholes and risk-neutral pricing.

Practise

Build the underlying intuition with finance and derivatives questions, and the probability that drives option value. If you are targeting an options market maker, the Akuna Capital question set is the place to start.