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好好学习向前进 · 2023年07月23日

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NO.PZ202108100100000301

问题如下:

Which of Doyle’s statements regarding the Eurodollar futures contract price is correct?

选项:

A.

Only Statement 1

B.

Only Statement 2

C.

Both Statement 1 and Statement 2

解释:

C is correct.

Doyle’s first statement is correct. Unless the Eurodollar futures contract’s quoted price is equal to the no-arbitrage futures price, there is an arbitrage opportunity. Moreover, if the quoted futures price is less than the no arbitrage futures price, then to take advantage of the arbitrage opportunity, the Eurodollar futures contract should be purchased and the underlying Eurodollar bond should be sold short. Doyle would then lend the short sale proceeds at the risk-free rate. The strategy that comprises those transactions is known as reverse carry arbitrage.

Doyle’s second statement is also correct. Based on the cost of carry model, the futures price is calculated as the future value of the sum of the underlying plus the underlying carry costs minus the future value of any ownership benefits. If the Eurodollar bond’s interest payment was expected in five months instead of two, the benefit of the cash flow would occur three months later, so the future value of the benefits term would be slightly lower. Therefore, the Eurodollar futures contract price would be slightly higher if the Eurodollar bond’s interest payment was expected in five months instead of two months.

A is incorrect because Doyle’s Statement 2 is correct (not incorrect). Based on the cost of carry model, the futures price would be higher if the underlying Eurodollar bond’s interest payment took place in five months instead of two months.

B is incorrect because Doyle’s Statement 1 is correct (not incorrect). If the Eurodollar’s futures contract price is less than the price suggested by the carry arbitrage model, the futures contract should be purchased.

中文解析:

表述1:由无套利模型定价得到的期货的价格是合理定价,现在市场上欧洲美元期货的价格低于这个合理定价,则买低卖高,因此应该买入,表述正确。

表述2:期货价格=FV(S0 +CC-CB),CC表示carry cost,CB表示carry benefit。

interest payment属于CB,如果利息支付发生在5个月而非2个月后,则CB的FV会因为后期复利的时间缩短了3个月而降低,考虑到CB作为减项,其减少将会导致期货价格上升,因此表述正确。

如果持有bond,在到期时用FP的价格卖出bond,不应该是FP越高越好么,为什么FP降价的时候买future呢?

1 个答案

Lucky_品职助教 · 2023年07月24日

嗨,努力学习的PZer你好:


持有债券的确应该希望未来价格越高越好。然而,在这种情况下,Doyle提到的买入期货是一种利用套利机会的策略,而不是为了持有债券。假设欧洲美元期货的价格低于根据套利模型计算得出的合理价格,那么购买期货合约并同时进行卖空欧洲美元债券的操作可以获得套利利润。

这种套利策略中,当市场上的期货价格低于合理价格时,购买期货合约意味着你以低于合理价格的价格买入了债券。然后你卖空欧洲美元债券,借来的债券卖出之后可以获取借出款项的利率收益。最后将借出的资金以无风险利率存入银行,并等待债券到期收回本金。这个过程中所获得的利润正是由于市场上期货价格低于合理价格所带来的套利机会。

所以,尽管从持有债券的角度来看,期货价格越高越好,但在这个特定的套利策略中,当市场上期货价格低于合理价格时,购买期货合约是为了利用套利机会获得利润。

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