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PZmomo · 2024年05月02日

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NO.PZ2023040701000039

问题如下:

Annisquam then develops a model that compares the value of a bond determined using a binomial interest rate tree to its value determined using spot rates. The bond he selects for the comparison is non-benchmark, option-free, has five years to maturity and an annual-pay coupon rate of 3%. The coupon rate is below the coupon rate of the benchmark bond. The yield curve is currently downward sloping. The output of Annisquam’s model shows that the spot rates generate a value equal to the market price of the bond, but the interest rate tree methodology produces a higher value.

Assuming Annisquam's spot rate valuation is correct, why does his model most likely produce a different result?

选项:

A.

The model is incorrect because both methodologies should value the bonds equally.

B.

He is valuing a non-benchmark bond.

C.

The yield curve is downward sloping.

解释:

Correct Answer: A

The binomial tree is based on the spot rate curve and a no arbitrage condition, therefore any option-free bond should have the same value whether using the spot rate curve or the binomial tree.

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1 个答案

品职答疑小助手雍 · 2024年05月03日

同学你好,Annisquam随后开发了一个模型,将使用二叉树确定的债券价值与使用spot利率确定的债券价值进行比较。他选择进行比较的债券是非基准债券,无期权,五年到期,年息为3%。票面利率低于基准债券的票面利率。收益率曲线目前是向下倾斜的。Annisquam模型的输出表明,spot rate计算出来的价值等于债券的市场价格,但二叉树方法产生的价值更高。

假设Annisquam的spot rate估值是正确的,为什么他的二叉树模型产生不同的结果?


结论就是:二叉树模型有误,因为这个模型计算结果应该和spot rate计算结果一致。