Gap Risk on a Knock-In FX Put
A UK exporter buys a one-year USD/GBP knock-in put from a bank to hedge USD 50m of receivables. The put has a strike of 0.78 GBP/USD and a knock-in barrier at 0.74. It pays intrinsic value at maturity if GBP/USD fixes below 0.78, but only if the barrier has been touched. The bank sells the option and delta-hedges in spot. The exporter’s treasury asks why the premium is much lower than a vanilla put. The bank’s risk report shows the option’s delta is small when spot is far above the barrier and becomes large and discontinuous near the barrier. Overnight, GBP/USD gaps from 0.741 to 0.732 after a political announcement, crossing the barrier. The bank’s hedge ratio was 0.35 before the gap. The bank must decide how to manage the position and what to tell the client.
1. Explain the payoff, why the premium is low, and how the gap affects the bank’s hedging.
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The option is a knock-in put: it only pays if GBP/USD touches 0.74 at some point and then fixes below 0.78 at maturity. If the barrier is never touched, the exporter receives nothing even if the maturity rate is below 0.78. That conditional payoff is why the premium is much lower than a vanilla put.
The delta is small while spot is far above the barrier, but it becomes large and discontinuous near the barrier. The bank sold the option, so it is short gamma: as spot falls towards 0.74, it must adjust its hedge quickly. A gap from 0.741 to 0.732 means the barrier is crossed without trading at the barrier. The bank cannot execute at 0.74; it only observes the jump and then must rehedge at worse prices. The hedge ratio of 0.35 before the gap is no longer appropriate because the option has become a vanilla put. The bank faces a loss from the gap and from the cost of establishing the new hedge.
2. Recommend how the bank should manage the risk and how the exporter should evaluate the hedge.
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The bank should charge a gap-risk premium and should not rely on continuous delta hedging near the barrier. It can use a static hedge, such as a vanilla put plus a digital or a barrier option, or set a wider spread and a barrier-monitoring process. It should stress the position for jumps through the barrier and for illiquid markets, and it should size limits to the worst gap. If the bank cannot hedge the gap, it should decline the trade or reduce the notional.
The exporter should evaluate the hedge against its actual exposure. The knock-in put is cheaper, but it leaves the exporter unprotected if GBP/USD ends below 0.78 without ever touching 0.74. That is a real basis risk, not a remote technicality. The exporter should compare the premium saving with the cost of a vanilla put, consider a knock-in with a rebate or a lower barrier, and decide whether the conditional cover is acceptable for its budget. It should also check that the barrier level and maturity match its receivable dates.