Considering the rapid development of cross‐border e‐commerce, this paper constructs a cross‐border dual‐channel supply chain with a supplier and a retailer in different countries. The supplier directly sells products to overseas market through an online channel and a retail channel. Since the supplier expands the overseas market and bears the potential risk of exchange rate volatility, the supplier is risk‐averse. In the presence of exchange rate volatility, the risk‐averse supplier decides whether to purchase an option to hedge against the risk of exchange rate volatility. Conditional value at risk is applied as a measure of the supplier's risk‐averse behavior. To identify the conditions under which the risk‐averse supplier should purchase an option, we analyze two scenarios: the benchmark model and the option model. By comparing the benchmark model with the option model, we show that if the option premium is lower than a threshold, the risk‐averse supplier prefers to purchase an option, which also makes the retailer better off. Interestingly, when the supplier becomes less risk‐averse, as the exchange rate volatility increases, both players benefit a higher utility in the option model. Finally, we verify the results’ robustness using numerical analysis.