# How to effectively hedge a Fixed-Term deal in a foreign currency?

Assume my firm is based in USD and agrees with some counterparty to buy, at time $T$, some quantity $Q$ of asset $A$ for a fixed price $K$.

Assume also that $A$ prices and $K$ are denominated in EUR.

Assume also that we have forward prices:

• For $A$, denotated by $F^A(t,T)$
• For the FX rate, denotated by $F^{FX}(t,T)$, expressed in USD per EUR.

Now my mark-to-market at time $t$ for this agreement is:

$$\text{MTM}_t = DF(t,T)\cdot Q\cdot( F^A(t,T) - K ) \cdot F^{FX}(t,T)$$

I would like to hedge my position for both FX and market effects, assuming I can get perfectly matching contracts for asset and FX in order to hedge.

I would sell $Q$ "lots" of to $F^A(t,T)$ hedge the dynamics of the hedge.

However, I'm unclear how much to hedge for the FX. Indeed, my FX exposure at time $t$ is $F^A(t,T) - K$, which can vary very much from $F^A(t-1,T) - K$ and hence results in an hedge completely off. So, what should be the amount to hedge in FX? I thought about $\mathbb{E}[ F^A(t,T) - K | \mathcal{F_{t-1}}]$ but my backtest doesn't give me good results at all.

Is there a common way of hedging this king of "spread" exposure?

You have already agreed to pay $QK$ EUR at $T$ to receive $Q$ units of A. If you sell $Q$ lots of $F^A(t,T)$ then you will receive $Q F^A(t,T)$ EUR and deliver $Q$ units of A. The combined flow is now just in EUR: at $T$ you receive a net of $Q(F^A(t,T)-K)$ EUR. You can hedge that by selling $Q(F^A(t,T)-K)$ of $F^{FX}(t,T).$ Then with both hedges, the net flow is just you receive $Q(F^A(t,T)-K)F^{FX}(t,T)$ USD at $T$.