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Yaooo · 2023年05月17日

不理解A为了含权债券而修正二叉树及如何修正

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NO.PZ201602270200001805

问题如下:

5. A benefit of performing Task 1 is that it:

选项:

A.

enables the model to price bonds with embedded options.

B.

identifies benchmark bonds that have been mispriced by the market.

C.

allows investors to realize arbitrage profits through stripping and reconstitution.

解释:

A is correct.

Calibrating a binomial interest rate tree to match a specific term structure is important because we can use the known valuation of a benchmark bond from the spot rate pricing to verify the accuracy of the rates shown in the binomial interest rate tree. Once its accuracy is confirmed, the interest rate tree can then be used to value bonds with embedded options. While discounting with spot rates will produce arbitrage free valuations for option-free bonds, this spot rate method will not work for bonds with embedded options where expected future cash flows are interest-rate dependent (as rate changes impact the likelihood of options being exercised). The interest rate tree allows for the alternative paths that a bond with embedded options might take.

B is incorrect because calibration does not identify mispriced benchmark bonds. In fact, benchmark bonds are employed to prove the accuracy of the binomial interest rate tree, as they are assumed to be correctly priced by the market.

C is incorrect because the calibration of the binomial interest rate tree is designed to produce an arbitrage-free valuation approach and such an approach does not allow a market participant to realize arbitrage profits though stripping and reconstitution.

为什么为了含权债券而修正二叉树?二叉树不是设立好的么,然后在每一个时点判断是否行权即可。

提到修正,请问需要如何修正?我知道要试错,满足波动率及lognormal(但是可以按这些前提设立好),但怎样算是对的模型呢。如果说是能反应债券价值的,既然知道能反应债券价值了,那也不需要二叉树了,因为已经求得债券价值。

1 个答案

pzqa015 · 2023年05月19日

嗨,努力学习的PZer你好:


原理是这样的。二叉树不能用spot rate估值,所以我们要构造一个二叉树。

二叉树是基于对未来利率波动率的预期来构造的,在forward rate(当前spot rate所隐含的)的基础上考虑利率波动率,具体根据forward rate构造二叉树的过程,同学可以听一下基础课的视频。

构造好二叉树后,不知道是否是合适的,那么如何检验呢?是找一只不含权债,用spot rate计算它的arbitrage free price,然后,同样用构造好的二叉树对它估值,通过调整利率波动率等参数(通常说是calibration过程),让二叉树计算的这只不含权债价格,等于用spot rate 计算的价格,二者都是arbitrage free price。此时,这个二叉树时一个合格的二叉树,然后,用它来对含权债估值。

----------------------------------------------
虽然现在很辛苦,但努力过的感觉真的很好,加油!

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