FRM Part I · FRM Exam Part I · Exotic Options
A bank sells a binary option paying 10 if the stock finishes above 100 at maturity. To super-replicate it conservatively (payoff never below the binary's), it buys 5 call spreads, each long a call struck at 98 and short a call struck at 100. Calls cost 7.90 (K=98) and 6.50 (K=100). What is the cost of this hedge?
The hedge costs 7.00. Each 98/100 call spread costs 1.40 and pays up to 2, so five spreads are needed to cover the 10 payoff, giving 5 × 1.40 = 7.00. This over-hedges the binary around the strike.
- A1.40
- B6.00
- C7.00Correct
- D14.00
Explanation
Each spread pays 2 for S ≥ 100 and between 0 and 2 for S between 98 and 100. Five spreads pay 10 for S ≥ 100 and more than 0 below 100 down to 98, so they dominate the binary. Cost = 5 × (7.90 − 6.50) = 5 × 1.40 = 7.00. Using 10 spreads would give 14.00 (wrong scale), and 1.40 is a single spread.
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