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Options interview questions

Trading interviews expect fluency with option payoffs, put–call parity, the Greeks and quick pricing approximations. These questions cover the ideas that come up most, from delta hedging to Black–Scholes.

32 sample questions with solutions. Edge has 449 options problems to practice, with a daily puzzle, timed games and a mock assessment. Practice them free.

1Roughly what is the delta of an at-the-money call with a short time to expiry?

  1. 0.25
  2. 0.5
  3. 0.75
  4. 1.0

Warm-up

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Answer: 0.5

Near the money the option is close to a coin flip, so delta ≈ 0.5.

2Which is put–call parity for European options on a non-dividend stock?

  1. C + P = S + K
  2. C − P = S − Ke^(−rT)
  3. C − P = K − S
  4. C = P

Warm-up

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Answer: C − P = S − Ke^(−rT)

Long call plus short put pays S_T − K at expiry, the same as a forward.

3Buying a straddle (call + put, same strike) is mainly a bet that…

  1. the price rises
  2. the price falls
  3. the price moves a lot either way
  4. rates rise

Warm-up

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Answer: the price moves a lot either way

A straddle profits from large moves, so it is long volatility.

4The theta of a long vanilla option is usually…

  1. positive
  2. negative
  3. zero
  4. equal to gamma

Warm-up

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Answer: negative

Time decay erodes value, so theta is negative for the holder.

5A deep in-the-money call has a delta close to…

  1. 0
  2. 0.5
  3. 1
  4. −1

Warm-up

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Answer: 1

It will almost surely be exercised, so it moves one-for-one with the stock.

6A put's delta lies in which range?

  1. 0 to 1
  2. −1 to 0
  3. −0.5 to 0.5
  4. 1 to 2

Warm-up

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Answer: −1 to 0

Put delta = call delta − 1, so it lies between −1 and 0.

7The gamma of a long option position (call or put) is…

  1. positive
  2. negative
  3. zero
  4. positive for calls, negative for puts

Warm-up

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Answer: positive

Long options are long convexity, so gamma is positive for both calls and puts.

8A call spread (long a K₁ call, short a K₂ call, K₁ < K₂) has a maximum payoff of…

  1. unlimited
  2. K₂ − K₁
  3. the premium paid
  4. zero

Warm-up

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Answer: K₂ − K₁

Above K₂ the payoff is flat at K₂ − K₁.

9The delta of an at-the-money straddle is approximately…

  1. 0
  2. 0.5
  3. 1
  4. −1

Warm-up

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Answer: 0

≈ 0.5 + (−0.5) = 0.

10Which position has unlimited potential loss?

  1. Long call
  2. Long put
  3. Short call
  4. Short put

Warm-up

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Answer: Short call

A short call loses more the higher the stock rises, with no cap.

11As expiry approaches, the time value of an out-of-the-money option…

  1. grows
  2. goes to zero
  3. stays constant
  4. doubles

Warm-up

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Answer: goes to zero

An OTM option has no intrinsic value, so it decays to zero.

12Implied volatility is…

  1. the historical standard deviation of returns
  2. the volatility that makes the model price equal the market price
  3. the VIX index
  4. the strike divided by spot

Warm-up

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Answer: the volatility that makes the model price equal the market price

Invert the pricing model on the market price to get implied vol.

13What is the price of a European call with strike 0 on a stock that pays no dividends?

  1. 0
  2. The stock price
  3. The strike
  4. It can't be priced

Warm-up

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Answer: The stock price

With K = 0 you always exercise and receive the stock, so the call is worth S.

14Zero rates, no dividends. Stock $90, a $90 call costs $6.34. What should the $90 put with the same expiry cost?

Put–call parityWarm-up

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Answer: 317/50 ≈ 6.34

A long call plus a short put pays S − K at expiry no matter what, the same as owning the stock and owing K. With zero rates their prices must match: C − P = S − K. So P = C − S + K = 6.34 − 90 + 90 = $6.34.

15Zero rates, no dividends. Stock $90, a $90 put costs $6.34. What should the $90 call with the same expiry cost?

Put–call parityWarm-up

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Answer: 317/50 ≈ 6.34

A long call plus a short put pays S − K at expiry no matter what, the same as owning the stock and owing K. With zero rates: C − P = S − K. So C = P + S − K = 6.34 + 90 − 90 = $6.34.

16You buy a $50 straddle for a total premium of $3.5. What is the upper breakeven stock price at expiry?

StrategiesWarm-up

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Answer: 107/2

A straddle pays |S − K| at expiry. You only profit once the move from $50 covers the $3.5 you paid, so the upper breakeven is 50 + 3.5 = 53.5.

17You buy a $50 straddle for a total premium of $3.5. What is the lower breakeven stock price at expiry?

StrategiesWarm-up

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Answer: 93/2

A straddle pays |S − K| at expiry. On the downside the stock must fall far enough below $50 to cover the $3.5 premium: 50 − 3.5 = 46.5.

18You are long 1 call contract (100 shares each), delta 0.4. How many shares must you sell to be delta-neutral?

Delta hedgingWarm-up

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Answer: 40

Each contract covers 100 shares, so your delta is 1 × 100 × 0.4 = 40 shares' worth of exposure. Selling that many shares cancels it.

19You are long 1 put contract (100 shares each), delta −0.4. How many shares must you buy to be delta-neutral?

Delta hedgingWarm-up

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Answer: 40

Puts gain when the stock falls, so their delta is negative: 1 × 100 × (−0.4) = −40 shares. Buying 40 shares brings the total to zero.

20Zero rates, no dividends. Stock $90, a $95 call costs $4.32. What should the $95 put with the same expiry cost?

Put–call parityWarm-up

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Answer: 233/25 ≈ 9.32

A long call plus a short put pays S − K at expiry no matter what, the same as owning the stock and owing K. With zero rates their prices must match: C − P = S − K. So P = C − S + K = 4.32 − 90 + 95 = $9.32.

21Which Greek spikes for an at-the-money option close to expiry?

  1. Rho
  2. Vega
  3. Gamma
  4. Theta of a deep ITM option

Interview

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Answer: Gamma

Delta jumps from 0 to 1 across a narrow price range, so gamma is huge.

22If implied volatility doubles, an at-the-money option's price roughly…

  1. stays the same
  2. doubles
  3. quadruples
  4. halves

Interview

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Answer: doubles

ATM price ≈ 0.4 · S · σ · √T, linear in σ.

23Vega is largest for which option?

  1. Deep ITM, short-dated
  2. ATM, long-dated
  3. Deep OTM, short-dated
  4. All are equal

Interview

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Answer: ATM, long-dated

Vega ∝ S·φ(d₁)·√T, largest for ATM long-dated options.

24Long a call and short a put at the same strike and expiry is equivalent to…

  1. a straddle
  2. a synthetic long forward
  3. a covered call
  4. a butterfly

Interview

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Answer: a synthetic long forward

Payoff S_T − K in every state, which is a long forward.

25Holding everything else fixed, higher interest rates make a call…

  1. cheaper
  2. more expensive
  3. unchanged
  4. worthless

Interview

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Answer: more expensive

A higher rate lowers the present value of the strike, raising the call price (positive rho).

26On equity indices, implied volatility is typically higher for…

  1. high strikes
  2. low strikes
  3. the ATM strike
  4. all strikes equally

Interview

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Answer: low strikes

The equity skew: downside puts trade at higher implied vol.

27Long stock plus a short call has the same payoff shape as…

  1. a long put
  2. a short put
  3. a long call
  4. a straddle

Interview

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Answer: a short put

A covered call caps the upside and keeps the downside, like a short put.

28Estimate the price of an at-the-money call: spot $50, implied vol 10%, 1 year to expiry, zero rates.

ATM approximationInterview

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Answer: 1.994

0.4 × 50 × 0.1 × √1 ≈ 2 (exact Black–Scholes 1.994).

29A delta-hedged position has gamma 0.02 per share. The stock moves $1. Approximately how much does the hedged position gain, per share?

GammaInterview

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Answer: 1/100 ≈ 0.01

Delta hedging cancels the first-order (straight-line) P&L. What's left is the curvature term from a Taylor expansion: ½ × Γ × (ΔS)² = ½ × 0.02 × 1² = 0.01. Long gamma gains whichever way the stock moves.

30Estimate the price of an at-the-money call: spot $50, implied vol 30%, 6 months to expiry, zero rates.

ATM approximationInterview

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Answer: 4.224

0.4 × 50 × 0.3 × √0.5 ≈ 4.243 (exact Black–Scholes 4.224).

31Black–Scholes call price: spot $100, strike $80, vol 15%, 1 year to expiry, rate 5%. (To the cent.)

Black–ScholesHard

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Answer: 24.08

Call = S N(d₁) − K e^(−rT) N(d₂) ≈ $24.08.

  1. Inputs: S = 100, K = 80, σ = 0.15, T = 1, r = 0.05.
  2. d₁ = [ln(S/K) + (r + σ²/2)T] / (σ√T) = [0.2231 + 0.06125] / 0.15 ≈ 1.896.
  3. d₂ = d₁ − σ√T ≈ 1.746. The discount factor is e^(−rT) ≈ 0.9512.
  4. Call = S N(d₁) − K e^(−rT) N(d₂) = 100 × 0.971 − 80 × 0.9512 × 0.9596 ≈ $24.08.

32Black–Scholes call price: spot $100, strike $80, vol 30%, 1 year to expiry, rate 0%. (To the cent.)

Black–ScholesHard

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Answer: 23.53

Call = S N(d₁) − K e^(−rT) N(d₂) ≈ $23.53.

  1. Inputs: S = 100, K = 80, σ = 0.3, T = 1, r = 0.
  2. d₁ = [ln(S/K) + (r + σ²/2)T] / (σ√T) = [0.2231 + 0.045] / 0.3 ≈ 0.8938.
  3. d₂ = d₁ − σ√T ≈ 0.5938. The discount factor is e^(−rT) ≈ 1.
  4. Call = S N(d₁) − K e^(−rT) N(d₂) = 100 × 0.8143 − 80 × 1 × 0.7237 ≈ $23.53.