题目理解

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？

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

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。

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​