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aileen20180623 · 2023年02月19日

这题是我没看全?

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NO.PZ201602270200001802

问题如下:

2. Based on Exhibits 1 and 2, the exchange that reflects the arbitrage-free price of the bond is:

选项:

A.

Eurex.

B.

Frankfurt.

C.

NYSE Euronext.

解释:

C is correct.

The bond from Exhibit 1 is selling for its calculated value on the NYSE Euronext exchange. The arbitrage-free value of a bond is the present value of its cash flows discounted by the spot rate for zero coupon bonds maturing on the same date as each cash flow. The value of this bond, 103.7815, is calculated as follows:

Notes:

1. Spot rates calculated using bootstrapping; for example: Year 2 spot rate ( Z2 ): 100=1.5/1.0125+101.5/(1+Z2)2=0.015019 100=1.5/1.0125+101.5/{(1+Z_2)}^2=0.015019

2. Present value calculated using the formula PV=FV/(1+r)n PV=FV/{(1+r)}^n,where n= number of years until cash flow, FV= cash flow amount, and r= spot rate.

A is incorrect because the price on the Eurex exchange, €103.7956, was calculated using the yield to maturity rate to discount the cash flows when the spot rates should have been used. C is incorrect because the price on the Frankfurt exchange, €103.7565, uses the Year 3 spot rate to discount all the cash flows.

考点:Introduction of Arbitrage Free Valuation

债券的无套利价格是用spot rate对债券的现金流进行折现得到的。

Exhibit 2中给的是1,2,3年期的Par rates,因此通过Bootstrapping的方式,由前向后推导出各个spot rate。已知1-year par rate等于1.25%,则1-year spot rate也等于1.25%

第二年spot rate计算:

100= 1.5/1.0125 + 101.5/(1+ Z2 )^2,所以Z2 =1.5019%

同理,我们可以计算出第三年的Spot rate:

100= 1.7/1.0125 + 1.7/ (1.015019)^2 + 101.7/(1+ S3)^3,所以Z3 =1.7049%

算得债券的价值为103.7815,所以NYSE Euronext这个交易所定价是合理的。

这题目问啥呢?‘Exhibit 4 presents most of the data of the implied values for a four-year, option-free, annual pay bond with a 2.5% coupon based on the information in Exhibit 3.。

答案我也没看懂,怎么算的?

1 个答案

pzqa015 · 2023年02月23日

嗨,爱思考的PZer你好:


题目问的是,根据表1和表2 ,哪个交易所的价格是无套利价格。

提到无套利价格,就要用spot rate或者二叉树来折现,由于题目到这里还没提利率波动和二叉树的事,所以要用spot rate来计算。

spot rate题目也没直接给,而是表2给了ytm。那么要用spot rate与ytm之间的关系来计算spot rate。

答案里面计算出spot rate 1是1.25%,spot rate2是1.5019%,spot rate3是1.7049%。

分别用这三个spot rate作为折现率,计算三个交易所的无套利价格

Eurex的价格是103.7959、NYSE的价格是103.7815、Frank的价格是103.7565,所以,NYSE的价格是无套利价格,选择C选项。


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