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KKII · 2024年05月11日

A、C选项辛苦解析一下

NO.PZ2023040701000050

问题如下:

Zhong asks, “Except using spot rate, are there other ways to calculate the arbitrage-free value of a bond?” Goll responds, “Yes, the arbitrage-free value of a bond can also be calculated using a binomial interest rate tree, where the interest rate tree provides a representation of how one-year forward rates evolve based on an interest rate model that identifies factors with predictable paths, an interest rate volatility assumption, and where forward rates on the tree are consistent with the current benchmark yield curve.”

Goll’s response to Zhong’s question is least likely correct with respect to:

选项:

A.

the interest model.

B.

interest rate volatility.

C.

the benchmark yield curve.

解释:

Correct Answer: A

Goll’s response to Zhong is incorrect with respect to the interest rate model. Goll states that the factors in the interest rate model must have predictable paths, which is incorrect. The factors that explain the dynamics of interest rates are random or stochastic. Goll is correct regarding the assumption of interest rate volatility and the current benchmark yield curve.

A选项,利率路径为啥不是predictable?


任何分叉路,上涨利率和下跌利率差距为e^(2σ),i(H)=i(L)*e^(2σ),同时middle forward rate = implied one period forward rate


只要知道i0,就能把后面的利率二叉树全给预测出来



C选项:只有middle forward rate和当前的benchmark yield curve一致,题干说所有的middle forward rate和当前的benchmark yield curve一致这明显是错的吧

3 个答案

pzqa31 · 2024年05月13日

嗨,努力学习的PZer你好:


利率二叉树上的远期利率需要与当前基准收益率曲线保持一致,以确保模型生成的资产价格路径与市场预期相符。换句话说,如果二叉树模型中的远期利率与基准收益率曲线不一致,那么模型生成的资产价格路径就可能偏离市场实际情况,从而导致模型预测结果的不准确。

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pzqa31 · 2024年05月13日

嗨,努力学习的PZer你好:


你说的是算middle rate的方法,那利率二叉树上利率是怎么来的?波动率又是从何而来?还是要基于假设和模型。其中利率路径取决于模型的假设。


回忆一下构造Binomial interest rate tree 的 requirements有三个:

  1. Current benchmark interest rate。即要有当前的yield curve
  2. assumption regarding the interest rate model,对利率模型的假设
  3. assumption about interest rate volatility,波动率的假设



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就算太阳没有迎着我们而来,我们正在朝着它而去,加油!

pzqa31 · 2024年05月12日

嗨,爱思考的PZer你好:


A选项错在predictable path,interest rate model一般采用lognormal model。利率的路径既取决于趋势项也取决于随机扰动项,所以是random的,并不是可以预测的。


C不能算错,整个forward rate on the tree的期望是等于 benchmark yield的。

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2024-04-21 20:58 1 · 回答

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2023-09-30 22:20 2 · 回答