FX Option Structure for a USD Receivable
A European industrial exporter has just signed a contract to receive USD 12 million in three months. The current EUR/USD spot rate is 1.0900 and the three-month forward is 1.0875. The treasurer wants to protect the euro value of the receipt, but the board has approved a maximum option premium of 0.8% of the USD notional. A three-month EUR call/USD put at a strike of 1.0850 costs 1.10% of notional. A 1.0800 strike costs 0.72%. A zero-cost collar can be structured by buying the 1.0850 EUR call and selling a EUR put at 1.0600. Implied volatility is 7.5%, and the risk reversal shows EUR puts trading at a slight premium to EUR calls. The company reports in euros and has no other USD receipts. The CFO is uncomfortable with any structure that gives up upside if the euro weakens, but the treasurer notes that the forward is already below spot.
1. Calculate the premium in USD and EUR for the 1.0850 call and the 1.0800 call, and identify which fits the board's 0.8% limit.
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For the 1.0850 EUR call: premium = 1.10% × $12,000,000 = $132,000. Converting at the 1.0900 spot rate gives $132,000 ÷ 1.0900 = €121,101. For the 1.0800 call: premium = 0.72% × $12,000,000 = $86,400, or $86,400 ÷ 1.0900 = €79,266. The board limit is 0.8% × $12,000,000 = $96,000, equivalent to €88,073. The 1.0850 call is above the limit; the 1.0800 call is within it. The zero-cost collar requires no premium but involves selling a EUR put at 1.0600.
2. Compare the euro receipts at expiry under the collar and the outright 1.0800 call at spot rates of 1.0500, 1.0900 and 1.1300. Show the payoff logic.
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Collar (buy 1.0850 call, sell 1.0600 put, zero premium): At 1.0500, the sold put is exercised, so the exporter sells USD at 1.0600: €12m ÷ 1.0600 = €11.3208m. At 1.0900, neither option is exercised: €12m ÷ 1.0900 = €11.0092m. At 1.1300, the bought call is exercised at 1.0850: €12m ÷ 1.0850 = €11.0599m. The collar therefore floors the receipt at about €11.06m and caps it at about €11.32m.
Outright 1.0800 call (premium €79,266): At 1.0500, the option is not exercised: €12m ÷ 1.0500 = €11.4286m, less premium €0.0793m = €11.3493m. At 1.0900: €11.0092m − €0.0793m = €10.9299m. At 1.1300, exercise at 1.0800: €11.1111m − €0.0793m = €11.0318m. The outright call has a lower floor (about €11.03m) but retains more benefit if the euro weakens.
3. Recommend a structure, addressing the CFO's concern about giving up upside and the board's premium limit.
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The 1.0850 call breaches the premium limit, so the realistic choices are the 1.0800 outright call, the zero-cost collar, or a forward. The forward at 1.0875 gives €12m ÷ 1.0875 = €11.0345m with certainty. The 1.0800 call gives a slightly lower floor after premium (about €11.03m) but preserves upside if EUR/USD falls towards 1.05; however, the premium is a sunk cost and the board may dislike paying it. The collar gives a better floor of about €11.06m and no premium, but caps the receipt at about €11.32m if the euro weakens sharply. Given the board's 0.8% premium cap and the CFO's reluctance to pay premium, the collar is the strongest fit, but the CFO must accept the cap. If giving up upside is unacceptable, use the 1.0800 call and absorb the 0.72% premium, or simply use the forward and remove uncertainty.