Explain delta, gamma, theta and vega.
Each Greek measures how an option's price responds to one input. For an at the money call on a $100 stock, delta 0.5 means a $1 rise adds $0.50, gamma 0.03 lifts delta to 0.53, theta costs $0.03 daily, and vega adds $0.20 per point.
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Example answer
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The greeks measure how an option's price changes. Delta is the change in the option's price for a $1 move in the stock. Gamma is how fast delta changes when the stock moves.
Theta is time decay, so options lose value over time. Vega is the sensitivity to volatility. Traders use all four to manage the risk of an options position, so you need to know them.
What holds it back
Delta and gamma are defined, but theta and vega are only named. There are no signs and no position, so the interviewer can't tell whether the speaker knows which way each one cuts.
The greeks measure how an option's price changes when one input moves and the others stay fixed. I'll use a long call as my example. Delta is the change in the option's price for a $1 move in the stock. For a call it's between 0 and 1, so if the stock goes up the call gains. Gamma is how fast delta changes when the stock moves. For a long option it's positive. Gamma is highest at the money and close to expiry. Theta is time decay, the change in price as one day passes. For a long call it's negative, and it speeds up as expiry gets close. Vega is the change in price for a one point move in implied volatility. For a long option it's positive, because more volatility means a bigger chance of a large payoff. So a long call is long delta, long gamma, long vega and short theta. If I sold the call, every sign would flip.
The greeks measure how an option's price changes when one input moves and the others stay fixed. I'll use a long call as my example, an at-the-money call on a $100 stock with three months left and implied volatility of 25%, worth about $5. The numbers are rounded for illustration. Delta is the change in the option's price for a $1 move in the stock. For a call it's between 0 and 1, and here it's about 0.5, so if the stock goes up $1 the call gains about 50 cents. It's also the hedge ratio. Against calls on 100 shares I'd short about 50 shares. Gamma is how fast delta changes when the stock moves. For a long option it's positive. With a gamma of 0.03, a $1 rise takes delta from 0.50 to 0.53. Gamma is highest at the money and close to expiry, which is when a hedge needs the most adjusting. Theta is time decay, the change in price as one day passes. For a long call it's negative, here about minus 3 cents a day, and it speeds up as expiry gets close. Vega is the change in price for a one point move in implied volatility. For a long option it's positive, because more volatility means a bigger chance of a large payoff while the loss is capped at the premium. Here it's about 20 cents, so if implied volatility goes from 25% to 26% the call is worth about $5.20. So a long call is long delta, long gamma, long vega and short theta. Theta is the rent I pay for gamma. If I delta hedge, I make money only when the stock moves more than the option's price implied. If I sold the call, every sign would flip.
The numbers, step by step
A long at-the-money call on a $100 stock, three months to expiry, 25% implied volatility and no interest, worth about $5. Greeks are rounded.
- Delta: gain if the stock rises $10.5 × $1
- $0.50
- Gamma: new delta after a $1 rise0.50 + 0.03
- 0.53
- Theta: change over one day−$0.03 × 1 day
- −$0.03
- Vega: gain if volatility rises 1 point$0.20 × (26 − 25)
- $0.20
- Call value at 26% volatility$5.00 + $0.20
- $5.20
What the interviewer listens for
- Can you define each greek as a change in price for a change in one input?
- Do you say which position you mean and give the right sign for each?
- Can you put a rough number on each one?
- Do you understand how they relate, especially gamma and theta?
Common mistakes
- Giving signs without saying whether the position is long or short.Gamma and vega are positive for a long option and negative for a short one.
- Saying vega measures the stock's volatility.It's the sensitivity to implied volatility, the level priced into the option, and the usual unit is one volatility point.
- Treating delta as fixed.It changes as the stock moves, which is what gamma measures and why a delta hedge has to be rebalanced.
- Reciting four definitions in a row with no example, so nothing shows that long gamma is paid for through theta.
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- What happens to bond prices when interest rates rise, and what is duration?
- Walk me through a DCF.
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