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我们 · 2020年04月17日

问一道题:NO.PZ2016070201000062

问题如下:

Suppose investors have interest rate expectations as illustrated in the decision tree below where the 1-year rate is expected to be 8%, 6%, or 4% in the second year and either 7% or 5% in the first year for a zero-coupon bond.

If investors are risk-neutral, what is the price of a $1 face value 2-year zero-coupon bond today?

选项:

A.

$0.88113.

B.

$0.88634.

C.

$0.89007.

D.

$0.89032.

解释:

Assuming investors are risk-neutral, the following decision tree illustrates the calculation of the price of a 2-year zero-coupon bond using the expected rates given. The expected price in one year for the upper node is $0.93458, calculated as $1 / 1.07. The expected price in one year for the lower node is $0.95238, calculated as $1 / 1.05. Thus, the current price is $0.89007, calculated as:

[0.5 x ($0.93458 / 1.06)] + [0.5 x ($0.95238 / 1.06)] = $0.89007

请问这个题为什么用不到second year的8%呢?为什么直接从first year 开始算?

2 个答案

品职答疑小助手雍 · 2020年04月20日

对的

品职答疑小助手雍 · 2020年04月18日

同学你好,因为8%那个衡量的其实已经是2-3年的利率了,和这个bond没有关系,只要考虑前两期的利率就行了。

我们 · 2020年04月20日

因为是算2-year zero coupon bond,所以用不到t=2时刻的利率(因为是forward rate),用t=1时刻的利率即可?