Delta Hedging USDJPY Options and Managing Premium Currency Exposure

Summary

The document explains the currency exposures involved in delta hedging a USDJPY option. In the example, a bank has sold a dollar put and calculates a short dollar hedge from the option’s delta. That hedge is paired with a long yen position at the prevailing exchange rate, so the hedge involves both currencies in the underlying pair. The option’s exercise settlement in yen does not change the basic approach of hedging its delta through USDJPY exposure.

The answer distinguishes this underlying hedge from any additional exposure created when the premium is received in another currency. If a European bank converts a dollar premium into euros and wants to manage its functional-currency risk, it can use EURUSD spot to adjust the dollar exposure as the delta hedge changes. This is a concise conceptual example, not a complete treatment of option risk management. It focuses on delta and currency conversion, without discussing gamma, vega, rebalancing costs, settlement conventions, or other risks that may matter in practice.

Key ideas

• A delta hedge in a currency pair creates exposure to both currencies in that pair.
• A short dollar hedge in USDJPY is accompanied by a long yen position at the spot rate.
• The option’s settlement currency does not replace the need to hedge its underlying pair exposure.
• A separate spot trade can manage dollar exposure against a bank’s functional currency.

Tags

# Which currency to hedge a position in FX options?


# Which currency to hedge a position in FX options?












Let's assume a bank sells to a client a put of \$1,000,000 dollars on USDJPY at 110 in 6 months. The delta of this put is -0.6, spot is 112. So to hedge its position the bank has to short \$600,000 dollars.

Two questions :

- Why couldn't the bank hedge in JPY as, if the client exercices, they will have to give him JPY instead of USD ?

- Does it change something if this option's prenium is in EUR ? Does the bank stil have to hedge in USD ?

## Answer by AlRacoon (score 4, accepted)

https://quant.stackexchange.com/a/49294

When you delta hedge a currency option, you are hedging in both currencies. In your example, since you have a short position of $600,000 as your hedge, this would be against JPY; therefore you would be long 600,000 * 112 = 67.2MM JPY at the same time.

Regarding your second question, you would still hedge the delta using the underlying of the option--in this case, USDJPY. However, if you are a European bank that converted the USD premium into EUR, your functional currency, and wanted to hedge out your USD risk, you could trade EURUSD spot to turn USD exposure back to EUR. You can adjust this risk as your delta hedge changes.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.