Using FX Call Spreads to Limit Losses While Retaining Some Upside

# Call spread hedge


# Call spread hedge












I'm trying to understand how a call spread is used for FX hedging. The example that my book gives is when we have USD receivables in 12 months which we want to convert to EUR and we want to hedge exchange rate risk. I understand how long EUR call position allows us to cap the maximum exchange rate but I have a problem with understanding how the hedge works when the spot is higher than the short strike. Then we'll have to sell EUR for the short strike price and we get to keep the difference between between the long and the short strike but it is not necessarily equal to the initial receivable. So we still have to convert the USD receivable to EUR using spot exchange rate, don't we? To me it looks more like a speculative position with capped potential profit rather than a hedge. Can someone please clarify what happens when the spot exchange rate is higher than both long and short strikes?

## Answer by AlRacoon (score 1, accepted)

https://quant.stackexchange.com/a/58423

The most risk free way to hedge FX risk is using a forward. So if you will receive 1 USD in the 1 Year, and you wanted to protect the EUR value of this receivable, you would sell USD/Buy EUR 1 year forward. If you sell the 1 Yr forward at 1.20USD/1EUR, when you receive 1 USD in a year, you would deliver it to your counterparty and receive 0.8333 EUR.

If you had a view that the USD would appreciate and wanted to benefit from this, you would not want to lock in the rate with a forward. Obviously you could just run this position unhedged and if you were right, you would benefit from the USD appreciation. Say the USD appreciates to 1 USD/EUR, you would receive 1 EUR in a years time. However, this would leave you exposed to any USD depreciation and you would receive less than the 0.8333 EUR in a years time if this were to happen.

This is where a call spread might be a useful hedge for you. Buy using a call spread, you could protect yourself from a large depreciation in the USD, and reduce the cost of this protection buy selling some of the upside from a USD appreciation. Often, these are done so the premiums of the long call and the short call offset each other so they are zero cost. This is commonly called a zero cost risk reversal.

Say you think the USD will appreciate up to 1 USD/EUR and not more. In this case, you could sell a USD Call/EUR Put where the strike is 1USD/EUR (giving up the appreciation of the USD beyond 1USD/EUR) and use the premium to buy the 1.40 USD Put/EUR Call to protect yourself if the USD were to depreciate. I am making the risk reversal strikes symmetrical for simplicity. In real life one of the premiums will be lower or higher and to make it a zero cost collar, the strikes would be adjusted to make the premiums net.

In a years time, one of the following 3 scenarios occur:

(1) The USD stays within your strikes of 1.40 USD/EUR and 1 USD/EUR. You would convert your 1 USD to EUR at the prevailing rate and benefit from any appreciation of the USD from 1.20 USD/EUR, and suffer losses from any depreciation of the USD from 1.20 USD/EUR. Recall 1.20 was the forward at the inception of the hedge.

(2) If the USD appreciates more than your strike short USD Call/EUR put strike of 1 USD/EUR, say to 0.9USD/EUR--you would be exercised on your short USD Call/EUR Put. The counterparty would Put 1 EUR or Call 1 USD at the strike of 1 USD/EUR, therefore you would sell your 1 USD and receive 1 EUR. You benefitted from the appreciation from the USD from 1.20 at the inception of the trade but capped the appreciation at 1 USD/EUR. Had you not sold the USD Call/EUR Put, you could have received 1.11 EUR from the market move.

(3) If the USD depreciates by more than your long USD Put/EUR call strike of 1.40, say to 1.50 USD/EUR--you would exercise your 1.40 strike USD Put/EUR Call. You would sell your USD at 1.40 USD/EUR and receive 0.714 EUR. You have suffered from the depreciation of the USD from 1.20 to 1.40. Had you not bought the USD Put/EUR Call, you would have only received 0.6666 EUR.

Net--you are exposed to the currency moves between 1.40 USD/EUR and 1 USD/EUR, enabling you to gain from any appreciation from 1.20 to 1 USD/EUR, and capping your losses from any depreciation greater than 1.40 USD/EUR.