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baoranjia · 2020年02月15日

问一道题:NO.PZ201602270200001805

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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.

老师,请问path dependence和interest rate dependence是两个概念是吗?前者需要正向计算,Monte Carlo method来解决,对应类似于MBS这种产品;后者binomial tree 即可解决,对应embedded option bond这种产品。这样理解正确?希望得到全面回答,感谢老师!

1 个答案

吴昊_品职助教 · 2020年02月16日

含权债券未来的现金流是会受到节点利率的影响,所以含权债券的现金流是interest rate dependent。解决这一类问题就需要我们在二叉树的每一个节点来判断一下,权利是否会被执行。一步一步从后往前推得到含权债券的价格。

像MBS这类产品,他们的现金流是path dependent的,也就是说他们的现金流不仅取决于这个点的利率水平,还取决于走过的利率路径。此时,就需要用蒙特卡洛模拟。考虑路径依赖,是蒙特卡洛模拟的优点。

你的理解没有什么问题。

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NO.PZ201602270200001805问题如下5. A benefit of performing Task 1 is thit:A.enables the mol to pribon with embeeoptions.B.intifies benchmark bon thhave been mispricethe market.C.allows investors to realize arbitrage profits through stripping anreconstitution.A is correct.Calibrating a binomiinterest rate tree to mata specific term structure is important because we cuse the known valuation of a benchmark bonfrom the spot rate pricing to verify the accuraof the rates shown in the binomiinterest rate tree. Onits accurais confirme the interest rate tree cthen useto value bon with embeeoptions. While scounting with spot rates will proarbitrage free valuations for option-free bon, this spot rate methowill not work for bon with embeeoptions where expectefuture cash flows are interest-rate pennt (rate changes impathe likelihooof options being exercise. The interest rate tree allows for the alternative paths tha bonwith embeeoptions might take. B is incorrebecause calibration es not intify mispricebenchmark bon. In fact, benchmark bon are employeto prove the accuraof the binomiinterest rate tree, they are assumeto correctly pricethe market. C is incorrebecause the calibration of the binomiinterest rate tree is signeto proarbitrage-free valuation approaansuapproaes not allow a market participant to realize arbitrage profits though stripping anreconstitution. 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。

2023-05-17 23:26 1 · 回答

NO.PZ201602270200001805 问题如下 5. A benefit of performing Task 1 is thit: A.enables the mol to pribon with embeeoptions. B.intifies benchmark bon thhave been mispricethe market. C.allows investors to realize arbitrage profits through stripping anreconstitution. A is correct.Calibrating a binomiinterest rate tree to mata specific term structure is important because we cuse the known valuation of a benchmark bonfrom the spot rate pricing to verify the accuraof the rates shown in the binomiinterest rate tree. Onits accurais confirme the interest rate tree cthen useto value bon with embeeoptions. While scounting with spot rates will proarbitrage free valuations for option-free bon, this spot rate methowill not work for bon with embeeoptions where expectefuture cash flows are interest-rate pennt (rate changes impathe likelihooof options being exercise. The interest rate tree allows for the alternative paths tha bonwith embeeoptions might take. B is incorrebecause calibration es not intify mispricebenchmark bon. In fact, benchmark bon are employeto prove the accuraof the binomiinterest rate tree, they are assumeto correctly pricethe market. C is incorrebecause the calibration of the binomiinterest rate tree is signeto proarbitrage-free valuation approaansuapproaes not allow a market participant to realize arbitrage profits though stripping anreconstitution. 三个老师能不能讲讲,我没看懂意思,可以逐一下吗?谢谢老师。

2023-01-30 16:27 1 · 回答

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2022-07-30 00:04 1 · 回答

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2021-03-07 18:27 1 · 回答

NO.PZ201602270200001805 请问该知识点在讲义哪,谢谢

2021-03-07 10:49 1 · 回答