题目
A stock index is valued at USD 800 and pays a continuous dividend at the rate of 3% per year. The 6-month futures contract on that index is trading at USD 758. The continuously compounded risk free rate is 2.5% per year. There are no transaction costs or taxes. Is the futures contract priced so that there is an arbitrage opportunity? If yes, which of the following numbers comes closest to the arbitrage profit you could realize by taking a position in one futures contract?
选项
A.38
B.40
C.42
D.There is no arbitrage opportunity
答案
B
解析
The no-arbitrage futures price should be: 800e(2.5%-3%)×0.5=798. Since the market price of the futures contract is lower than this price, there is an arbitrage opportunity. The futures contract could be purchased and the index sold. Arbitrage profit =798-758=40 无套利期货价格应为:800e^(((2.5% - 3%)×0.5)=798。由于期货合约的市场价格低于该价格，存在套利机会。买进期货合约，卖出指数。套利利润=798－758 = 40