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In this paper, we consider the optimal cross-hedging and risk control problem of a competitive firm facing exchange risk exposure in a multi-period setting. We present the optimal positions of currency futures and options to maximize the exponential utility of the terminal wealth by dynamic programming approach. To evaluate the potential effectiveness of cross-hedging with currency futures and options, we compare terminal wealth, utility based on terminal wealth and variance of the wealth accumulation path in three cases: hedging with futures and options, net futures hedging and no hedging. An empirical study of two cross-exchange rates of USD/EUR and CNY/USD is performed. The results show that cross-exchange rate futures and options always offer the firm an improved ability to hedge against the foreign exchange rate risks. Relative to no hedging, cross-hedging with currency futures and options or net currency futures hedging achieves positive returns. As the risk aversion coefficient increases, the firm's profit of futures hedging increases, while the profit of options hedging decreases. We suggest the firm with smaller risk aversion coefficient choose options hedging, and the firm with higher risk aversion coefficient choose futures hedging. Furthermore, when using currency derivatives for hedging, the wealth volatility also decreases significantly. Thus, for the multinational firms, cross-currency hedging is an efficient risk management technique to reduce their foreign exchange risk exposure. [ABSTRACT FROM AUTHOR]