How to solve Options basics questions

Put-call parity, spread and straddle payoffs, the at-the-money rule of thumb, time value and delta hedging. Rates are zero unless the question says otherwise.

How to solve them

Parity

1. Cue: you know one of call, put or stock and need another at the same strike.
2. Method: C - P = S - PV(K). With zero rates PV(K) = K.
3. Memory hook: long call + short put = long forward.
4. Check: an in-the-money call is worth more than the matching put.
5. Interviewers often follow up with "what if rates were 5%?" or "what happens if vol doubles?". Have the direction ready.

Payoffs

1. Cue: spreads, straddles, butterflies, "breakeven", "max profit".
2. Method: draw the payoff at expiry at each strike, then subtract what you paid.
3. Call spread max = width - cost. Fly max = wing width - cost. Straddle breakevens = K +/- total premium.
4. Interviewers often follow up with "what if rates were 5%?" or "what happens if vol doubles?". Have the direction ready.

Atm

1. Cue: "roughly", "at the money", vol and time given.
2. Method: ATM option = 0.4 x S x vol x sqrt(T).
3. Anchors: sqrt(1/4) = 0.5, sqrt(1/12) = 0.29, sqrt(1/52) = 0.14.
4. Check: doubling vol doubles the price, quadrupling time doubles it.
5. Interviewers often follow up with "what if rates were 5%?" or "what happens if vol doubles?". Have the direction ready.

Value

1. Cue: "intrinsic" or "time value".
2. Method: intrinsic = max(S - K, 0) for a call, max(K - S, 0) for a put. Time value is the rest of the price.
3. Check: time value is largest at the money.
4. Interviewers often follow up with "what if rates were 5%?" or "what happens if vol doubles?". Have the direction ready.

Delta

1. Cue: "delta neutral", "hedge".
2. Method: shares of exposure = contracts x 100 x delta. Trade the opposite in stock.
3. Long calls and short puts have positive delta. Short calls and long puts have negative delta.
4. Interviewers often follow up with "what if rates were 5%?" or "what happens if vol doubles?". Have the direction ready.

Worked examples

• Stock at 105. The 100-strike call trades at 6. How much of the price is time value? Answer to 2 decimals.

  Answer: 1

  1. Intrinsic value = max(S - K, 0) = max(105 - 100, 0) = 5.
  2. Time value = 6 - 5 = 1.00.

• Stock at 107, rates zero. The 102-strike call is 11.00. What is the 102-strike put worth? Answer to 2 decimals.

  Answer: 6

  1. Put-call parity: C - P = S - K.
  2. P = C - S + K = 11.00 - 107 + 102.
  3. P = 6.00.

• You buy the 80 straddle: the call for 2 and the put for 6. What is the upper breakeven at expiry? Answer to 2 decimals.

  Answer: 88

  1. Total premium = 2 + 6 = 8.
  2. The stock has to finish 8 away from 80: 88.

Firms that test this

Akuna Capital · SIG · IMC · Jane Street

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