开发者:上海品职教育科技有限公司 隐私政策详情

应用版本:4.2.11(IOS)|3.2.5(安卓)APP下载

shihong · 2022年02月09日

是不是低买高卖

NO.PZ2020012005000040

问题如下:

Suppose that F1 and F2 are the futures prices on the same commodity with maturities t1 and t2 with t2 > t1. Storage costs are negligible. The risk-free rate is R for all maturities. Use an arbitrage argument to show that:

F2F1(1+R)t2t1F_2\leq F_1(1+R)^{t_2-t_1}

解释:

A trader can enter into a long futures contract with maturity t1 and a short futures contract with maturity t2. At time t1 F1 is borrowed and the asset is bought for F1. The loan is repaid at time t2 and the asset is sold for F2.

The cash flows are

Time t1:F1+F1=0t_1: -F_1 + F_1 = 0, and

Time t2:F2F1(1+R)t2t1t_2: F_2 - F_1(1 + R)^{t_2 - t_1}

This simple strategy is certain to lead to a profit at time t2 if:

F2>F1(1+R)t2t1F_2 > F_1(1 + R)^{t_2 - t_1}

Thus, the prices will adjust such that:

F2F1(1+R)t2t1F_2 \leq F_1(1 + R)^{t_2 - t_1}

老师,您好。F2和F1调整无风险利率后的资产价值应该相等,题目中F2更小存在套利机会。那是不是应该低买高卖,longF2 shortF1 呀

2 个答案

李坏_品职助教 · 2022年02月17日

嗨,努力学习的PZer你好:


对 所有传统金融理论都有一个大前提:理性个人。就是每个投资者都是理性的,能够迅速挖掘出套利机会并且将套利空间抹平。所以理论上来说,市场上不可能有空手套白狼的机会

----------------------------------------------
努力的时光都是限量版,加油!

李坏_品职助教 · 2022年02月09日

嗨,努力学习的PZer你好:


这道题是为了证明题干结尾的结论成立。


首先,套利的本质是空手套白狼。

所以在t1时刻,先从银行借了一笔钱F1,买入资产F1;同时进入了一个空头期货合约


在t2时刻,首先要做的是归还贷款,贷款金额=F1*(1+r)^(t2 - t1),

然后将我们在t1时买入的资产进行交割,此外还可以收到一笔钱F2,

所以t2 时刻,我们的现金流就是F2-F1*(1+r)^(t2-t1)


如果定价出现了题干中的F2 > F1*(1+r)^(t2-t1),那这个现金流就是大于0的,但这是不可能出现的(因为金融市场不存在空手套白狼),所以F2一定小于等于右边。


----------------------------------------------
加油吧,让我们一起遇见更好的自己!

小王爱学习 · 2022年02月17日

金融市场不存在空手套白狼的原因是因为大家都不傻吗?如果只看公式是这么计算的,

  • 2

    回答
  • 0

    关注
  • 361

    浏览
相关问题

NO.PZ2020012005000040问题如下Suppose thF1 anF2 are the futures prices on the same commoty with maturities t1 ant2 with t2 t1. Storage costs are negligible. The risk-free rate is R for all maturities. Use arbitrage argument to show that:F2≤F1(1+R)t2−t1F_2\leq F_1(1+R)^{t_2-t_1}F2​≤F1​(1+R)t2​−t1​A trar center into a long futures contrawith maturity t1 ana short futures contrawith maturity t2. time t1 F1 is borroweanthe asset is bought for F1. The lois repaitime t2 anthe asset is solfor F2. The cash flows areTime t1:−F1+F1=0t_1: -F_1 + F_1 = 0t1​:−F1​+F1​=0, anTime t2:F2−F1(1+R)t2−t1t_2: F_2 - F_1(1 + R)^{t_2 - t_1}t2​:F2​−F1​(1+R)t2​−t1​This simple strategy is certain to leto a profit time t2 if:F2 F1(1+R)t2−t1F_2 F_1(1 + R)^{t_2 - t_1}F2​ F1​(1+R)t2​−t1​Thus, the prices will aust suthat: F2≤F1(1+R)t2−t1F_2 \leq F_1(1 + R)^{t_2 - t_1}F2​≤F1​(1+R)t2​−t1​这道题思路的出发点就没懂,怎么想到要借F1,买F1资产,而不是F2?为什呢不是从0时刻开始,而是从t1时刻开始?t1时刻建立的空头期货就是F2吗?能否画个图说一下这种题怎么想?

2024-06-04 22:30 2 · 回答

NO.PZ2020012005000040 问题如下 Suppose thF1 anF2 are the futures prices on the same commoty with maturities t1 ant2 with t2 t1. Storage costs are negligible. The risk-free rate is R for all maturities. Use arbitrage argument to show that:F2≤F1(1+R)t2−t1F_2\leq F_1(1+R)^{t_2-t_1}F2​≤F1​(1+R)t2​−t1​ A trar center into a long futures contrawith maturity t1 ana short futures contrawith maturity t2. time t1 F1 is borroweanthe asset is bought for F1. The lois repaitime t2 anthe asset is solfor F2. The cash flows areTime t1:−F1+F1=0t_1: -F_1 + F_1 = 0t1​:−F1​+F1​=0, anTime t2:F2−F1(1+R)t2−t1t_2: F_2 - F_1(1 + R)^{t_2 - t_1}t2​:F2​−F1​(1+R)t2​−t1​This simple strategy is certain to leto a profit time t2 if:F2 F1(1+R)t2−t1F_2 F_1(1 + R)^{t_2 - t_1}F2​ F1​(1+R)t2​−t1​Thus, the prices will aust suthat: F2≤F1(1+R)t2−t1F_2 \leq F_1(1 + R)^{t_2 - t_1}F2​≤F1​(1+R)t2​−t1​ 根据正常的物价上涨的逻辑来说,F2应该大于F1,所以存在套利机会,那就是在t1做空,借入期货,并卖掉得到资金,然后在t2卖掉期货,得到F2,然后支付F1(1+R)^(t2-t1)利息,得到F2-F1(1+R)^(t2-t1)的收益。这个理解对吗?但是答案中用现金流的方式不太理解,为什么time1现金流是这样。另外结论Thus, the prices will aust suthat:这里的公式应该如何理解呢

2024-03-09 00:49 2 · 回答

NO.PZ2020012005000040 问题如下 Suppose thF1 anF2 are the futures prices on the same commoty with maturities t1 ant2 with t2 t1. Storage costs are negligible. The risk-free rate is R for all maturities. Use arbitrage argument to show that:F2≤F1(1+R)t2−t1F_2\leq F_1(1+R)^{t_2-t_1}F2​≤F1​(1+R)t2​−t1​ A trar center into a long futures contrawith maturity t1 ana short futures contrawith maturity t2. time t1 F1 is borroweanthe asset is bought for F1. The lois repaitime t2 anthe asset is solfor F2. The cash flows areTime t1:−F1+F1=0t_1: -F_1 + F_1 = 0t1​:−F1​+F1​=0, anTime t2:F2−F1(1+R)t2−t1t_2: F_2 - F_1(1 + R)^{t_2 - t_1}t2​:F2​−F1​(1+R)t2​−t1​This simple strategy is certain to leto a profit time t2 if:F2 F1(1+R)t2−t1F_2 F_1(1 + R)^{t_2 - t_1}F2​ F1​(1+R)t2​−t1​Thus, the prices will aust suthat: F2≤F1(1+R)t2−t1F_2 \leq F_1(1 + R)^{t_2 - t_1}F2​≤F1​(1+R)t2​−t1​ 这题可否这么理解①以FP1价格long futures@t1@,以FP2价格short futures@t2;②在t1时刻找银行借cash FP1,进行支付,并得到spot;③持有spot到t2,在t2时刻把spot交出去,得到cash FP2;③归还银行借的本息和FP1*(1+R)^(t2-t1)当FP2>FP1*(1+R)^(t2-t1)时,套利获得收益,否则无收益

2023-12-08 10:22 1 · 回答

NO.PZ2020012005000040 问题如下 Suppose thF1 anF2 are the futures prices on the same commoty with maturities t1 ant2 with t2 t1. Storage costs are negligible. The risk-free rate is R for all maturities. Use arbitrage argument to show that:F2≤F1(1+R)t2−t1F_2\leq F_1(1+R)^{t_2-t_1}F2​≤F1​(1+R)t2​−t1​ A trar center into a long futures contrawith maturity t1 ana short futures contrawith maturity t2. time t1 F1 is borroweanthe asset is bought for F1. The lois repaitime t2 anthe asset is solfor F2. The cash flows areTime t1:−F1+F1=0t_1: -F_1 + F_1 = 0t1​:−F1​+F1​=0, anTime t2:F2−F1(1+R)t2−t1t_2: F_2 - F_1(1 + R)^{t_2 - t_1}t2​:F2​−F1​(1+R)t2​−t1​This simple strategy is certain to leto a profit time t2 if:F2 F1(1+R)t2−t1F_2 F_1(1 + R)^{t_2 - t_1}F2​ F1​(1+R)t2​−t1​Thus, the prices will aust suthat: F2≤F1(1+R)t2−t1F_2 \leq F_1(1 + R)^{t_2 - t_1}F2​≤F1​(1+R)t2​−t1​ 没看懂,请详解。谢谢老师。

2023-02-07 19:29 1 · 回答

NO.PZ2020012005000040 问题如下 Suppose thF1 anF2 are the futures prices on the same commoty with maturities t1 ant2 with t2 t1. Storage costs are negligible. The risk-free rate is R for all maturities. Use arbitrage argument to show that:F2≤F1(1+R)t2−t1F_2\leq F_1(1+R)^{t_2-t_1}F2​≤F1​(1+R)t2​−t1​ A trar center into a long futures contrawith maturity t1 ana short futures contrawith maturity t2. time t1 F1 is borroweanthe asset is bought for F1. The lois repaitime t2 anthe asset is solfor F2. The cash flows areTime t1:−F1+F1=0t_1: -F_1 + F_1 = 0t1​:−F1​+F1​=0, anTime t2:F2−F1(1+R)t2−t1t_2: F_2 - F_1(1 + R)^{t_2 - t_1}t2​:F2​−F1​(1+R)t2​−t1​This simple strategy is certain to leto a profit time t2 if:F2 F1(1+R)t2−t1F_2 F_1(1 + R)^{t_2 - t_1}F2​ F1​(1+R)t2​−t1​Thus, the prices will aust suthat: F2≤F1(1+R)t2−t1F_2 \leq F_1(1 + R)^{t_2 - t_1}F2​≤F1​(1+R)t2​−t1​

2022-10-27 21:35 1 · 回答