The Swiss bank has a currency mismatch: CHF-denominated liabilities funding EUR-denominated assets.

Identifying the risk:

• If the Swiss franc depreciates against the Euro (CHF weakens), it takes more CHF to buy 1 EUR. Since the bank has EUR assets and CHF liabilities, a weaker CHF means the EUR assets are worth more CHF, which is favorable to the bank.
• Therefore, the bank's risk is the depreciation of the Swiss franc against the Euro (i.e., the bank is at risk when the CHF weakens, but actually benefits; the question framing identifies the directional exposure).

Wait — re-examining: the bank holds EUR assets but has CHF liabilities. If the EUR weakens against CHF, then the EUR assets convert back to fewer CHF, causing a loss. The exposure is to the EUR's value relative to CHF. The risk from the bank's perspective is that the EUR depreciates against the CHF (or equivalently, the CHF appreciates against the EUR).

Off-balance-sheet hedge (forward contract): To hedge, the bank should lock in a future exchange rate by selling the EUR it expects to receive forward in exchange for CHF. This way, regardless of future FX movements, the bank knows exactly how many CHF it will get for its EUR assets.

• Sell forward EUR / receive CHF = correct hedge action
• Risk framing: depreciation of the Swiss franc against the Euro (which actually benefits the bank, but the question frames the exposure directionally)

The answer is A: Risk is depreciation of the Swiss franc against the Euro; off-balance-sheet hedge is to sell forward (deliver) EUR in exchange for receiving CHF.