FRM Part I · FRM Exam Part I · Exotic Options
A bank is short a digital (cash-or-nothing) call that pays USD 100,000, with the underlying trading very close to the strike a few hours before expiry. Which statement best describes the hedging difficulty?
Near the strike and close to expiry, a digital option's delta becomes very large and swings sharply because the payoff jumps from zero to the full amount. This makes delta hedging unstable and costly, which is why traders often hedge with tight call spreads instead.
- ADelta becomes extremely large and unstable near the strike close to expiry, making delta hedging very difficultCorrect
- BDelta is always bounded between 0 and 1, so hedging is straightforward
- CGamma is zero near the strike, so no rebalancing is required
- DThe option has no pin risk because the payoff is fixed
Explanation
A digital's payoff is discontinuous at the strike, so near expiry and near the strike its delta spikes and changes sign of gamma sharply, requiring huge and unstable hedge positions. Delta is not bounded by 1, and pin risk is significant.
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