问一道题：NO.PZ201602270200001901

问题如下：

1. Based on Exhibit 1, which of the following bonds most likely includes an arbitrage opportunity?

选项：

Bond A

Bond B

Bond C

解释：

B is correct.

Bond B’s arbitrage-free price is calculated as follows:

$frac3{1.02}+\frac{103}{1.02^2}=101.9416$

which is higher than the bond’s market price of 100.9641. Therefore, an arbitrage opportunity exists. Since the bond’s value (100.9641) is less than the sum of the values of its discounted cash flows individually (101.9416), a trader would perceive an arbitrage opportunity and could buy the bond while selling claims to the individual cash flows (zeros), capturing the excess value. The arbitrage-free prices of Bond A and Bond C are equal to the market prices of the respective bonds, so there is no arbitrage opportunity for these two bonds:

Bond A:

$frac1{1.02}+\frac{101}{1.02^2}=98.0584$

Bond C:

$frac5{1.02}+\frac{105}{1.02^2}=105.8247$