FRM Part I · FRM Exam Part I · Exotic Options
A dealer wants to replicate a long position in a cash-or-nothing call paying USD 1 using vanilla options. Which approximate static replication is most appropriate?
A binary call is approximated by a scaled long call spread with strikes just either side of the binary strike. It pays zero below the lower strike and the full amount above the upper strike, mimicking the step payoff. A short spread would reverse the exposure.
- AA long call spread with strikes just below and above the binary strike, scaled to give a USD 1 maximum payoffCorrect
- BA long straddle at the binary strike
- CA short call spread with strikes around the binary strike
- DA long butterfly centered at the binary strike
Explanation
Buying a call at K-e and selling a call at K+e, scaled by 1/(2e), pays zero below K-e, rises to 1 above K+e, approximating the step payoff. A short call spread gives the opposite exposure. Straddles and butterflies do not produce a step.
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