# Exposure of two companies in a transaction involving an FX option

An American company $$A$$ has sold a manufactured product to a German company $$B$$, and they agree for the payment of 100,000 EUR in 1 year.

1. What type of exposure does $$B$$ have?
2. What type of exposure does $$A$$ have?
3. What is the potential problem for $$A$$ if it decides not to hedge (i.e. not to cover)?
4. Repeat the exercise in case the payment is performed in USD.

Let $$K_T$$ be the exchange rate (EUR/USD) at time $$t=T$$ (1 year from now), and let $$K_0$$ be the exchange rate at time $$t=0$$ (i.e. now).

1. Since EUR is the domestic currency of $$B$$, it will take no risk in the transaction.
2. If $$A$$ buys a Forward contract (at time $$T$$ the firm $$A$$ will sell 100.000 EUR at a fixed rate $$K_F$$) but $$K_f < K_T$$, then it will face an indirect loss of 100,000*($$K_T - K_F$$) USD. If $$A$$ buys a Put option which gives it the right to sell 100.000 EUR at the rate $$K_P$$, it will exercise the option only if $$K_P > K_T$$, otherwise it will not exercise and will sell 100.000 EUR at the rate $$K_T$$.
3. If $$A$$ decides not to hedge, the potential problem is in the case $$K_T < K_0$$, because in this case $$A$$ will face an indirect loss of 100,000*($$K_0 - K_T$$) USD.
4. Since USD is the domestic currency of $$A$$, it will take no risk in the transaction. On the other hand, $$B$$ should buy a Call option, because it gives $$B$$ the right to buy 100,000 USD at time $$T$$ at a fixed rate $$K_C$$: $$B$$ will exercise the option if $$K_C > K_T$$, otherwise it will not exercise and will buy 100,000 USD at the rate $$K_T$$.

Is the reasoning correct?