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Bond Valuation using nodes and Trees

How do you know whether to add the coupon or not when valuing bonds using the nodes and decision trees?

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If I’m recalling the material correctly: the coupon amount is always taken into account as a component of a bond’s pv at a particular node (at least in the case of the problems presented and discussed in the curriculum). There are instances where you might adjust the coupon amount at a particular node if the bond you’re valuing contains an embedded floor or ceiling.

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You always add the coupon.

What might change is whether you’re interested in the value of the bond by itself or the value of the bond and the coupon together.

Do you have a specific example that’s vexing you?

I wrote a series of articles on creating and using binomial trees for fixed income: http://www.financialexamhelp123.com/binomial-trees-for-fixed-income/.

(Full disclosure: as of 4/25/16 there is a charge to read the articles on my website.  You can get an idea of the quality of the articles by looking at the free samples here: http://www.financialexamhelp123.com/sample-articles/.)

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I have been battling with this same issue for weeks. It seems about 50% of the BB and EOC’s I’m doing require you to add the coupon and the rest don’t. I can’t seem to identify the difference in the questions.

Here is an example for you Bill, Reading 36 EOC #13.

Based on Exhibits 3 and 4, the value of Bond C at the upper node at Time 1 is closest to:

  1. 97.1957.

  2. 99.6255.

  3. 102.1255.

Now exhibit 4 just shows that the bond we are working with has 2 years to maturity and pays a 2.5% coupon. (The title of exhibit 4 says this is an annual pay bond. This debunks my initial thoughts on this discrepancy being due to coupon paying vs zeros. Even this coupon paying bond won’t use the coupon in calculating the value.)

Exhibit 3 is the rate tree. Math goes:

(102.5/1.02885)+(102.5/1.02885)/2 then +2.5 gives us the value of 102.1255. This is the answer I chose, which was wrong. The answer is 99.6255, which is my answer -3. In other examples though the coupon is added to calculate the value, except when calculating the value at T=0 because there is no coupon at initiation. (Like EOC #14 right below this question) What is the difference??????? I’m going crazy. Thanks for the help!

Time 0
Time 1
Time 2

 
 
2.7183%

 
2.8853%
 

1.500%
 
1.6487%

 
1.7500%
 

 
 

1.0000%.

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S2000magician wrote:

You always add the coupon.

What might change is whether you’re interested in the value of the bond by itself or the value of the bond and the coupon together.

Do you have a specific example that’s vexing you?

I wrote a series of articles on creating and using binomial trees for fixed income: http://www.financialexamhelp123.com/binomial-trees-for-fixed-income/.

(Full disclosure: as of 4/25/16 there is a charge to read the articles on my website.  You can get an idea of the quality of the articles by looking at the free samples here: http://www.financialexamhelp123.com/sample-articles/.)

Note that, for the time being, there’s a 33% discount on the subscription rate.

Please see my example above if you would. Thank You.

I bathe in Lake Superior Returns

In any pricing model based on binomial or trinomial trees, in the nodes of the tree you put all the cashflows you want to price. So if the goal is to price the bond as a whole (not stripped of its coupon), you must include all the coupons in the nodes.

asrmek wrote:
S2000magician wrote:
You always add the coupon.

What might change is whether you’re interested in the value of the bond by itself or the value of the bond and the coupon together.

Do you have a specific example that’s vexing you?

I wrote a series of articles on creating and using binomial trees for fixed income: http://www.financialexamhelp123.com/binomial-trees-for-fixed-income/.

(Full disclosure: as of 4/25/16 there is a charge to read the articles on my website.  You can get an idea of the quality of the articles by looking at the free samples here: http://www.financialexamhelp123.com/sample-articles/.)

Note that, for the time being, there’s a 33% discount on the subscription rate.

Please see my example above if you would. Thank You.

In your example you say that the correct answer is your answer less 3.  Actually, it’s your answer less 2.5, which is the coupon.

The key here is that the question asks you to value the bond, not the bond and the coupon payment that occurs on that date; that’s why you don’t add the coupon.  You would want to know the value of the bond alone if, for example, it is callable or putable and you’re trying to determine whether the option holder would exercise the option at that time; as the coupon has to be paid whether or not the option is exercised, the decision to exercise depends only on the value of the bond, not on the value of the bond plus the coupon.

Simplify the complicated side; don't complify the simplicated side.

Financial Exam Help 123: The place to get help for the CFA® exams
http://financialexamhelp123.com/