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明明要加油 · 2023年09月07日

请问老师，能不能帮我写一下，如何用par rate推导出spot rate呢？

  1. CFA II
  2. Fixed Income

NO.PZ2018123101000113

问题如下：

Thames reminds Cromwell that her model assumes zero interest rate volatility and a flat government yield curve. Cromwell responds that Thames should relax these unrealistic assumptions. Thames outlines the steps to take in valuing risky bonds under this scenario in Exhibit 1.

EXHIBIT 1 STEPS IN VALUING RISKY BONDS, ARBITRAGE-FREE FRAMEWORK


Which step in Exhibit 1 regarding valuing risky bonds has Thames most likely outlined correctly?

选项：

A.

Step 1.

B.

Step 2.

C.

Step 3.

解释：

Thames is correct in describing Step 3 but incorrect about both Step 1 and Step 2.

The third point in Step 1 is explained incorrectly. The par curve where each bond is priced at par value, not the spot curve, is used to derive implied zero-coupon rates. In the second point of Step 2, she is incorrect regarding the recovery rate. The assumption is not based on credit ratings. The recovery rate if default were to occur should conform to the seniority of the debt issue and the nature of the issuer’s assets. For instance, a firm with a high ratio of assets relative to the debt level and debt senior in the capital structure will result in a higher recovery for bondholders than one with the reverse situation.

如题，感谢。

或者老师有基础班何老师手写的推导步骤截屏吗～这块我不明白。谢谢老师

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吴昊_品职助教 · 2023年09月07日

嗨，努力学习的PZer你好：


我们知道了一年的par rate，也相当于知道了一年期的spot rate。

我们知道了两年的par rate，也就相当于知道了分子的coupon是par rate，用1年期的spot rate和两年期的spot rate折现两笔现金流，使其等于面额par。由于已经知道了1年期的spot rate，所以两年期的spot rate可求出。

再将1年期的spot rate，和已经求出的2年的spot rate代入一个三年期的coupon-paying bond，由于已经知道了coupon是par rate，pv是面值，所以就可以求出三年的spot rate。以此类推，我们就算出了各期的spot rate

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努力的时光都是限量版，加油！

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