Calculating Node value in binomial interest rate tree

[SpareTime]

In the CFA Curriculum they do not discount the coupon payment when calculating the value of a node. Here is an example, where they are taking the average of the two nodes to the right. However, the 2.5 is outside the bracket and is not discounted by the 1 year node rate, 1.4925%.

Value =0.5 × [(104.0168/1.014925 + 104.6350/1.014925)] + 2.5=0.5 × [102.4872 + 103.0963] + 2.5=105.2917

Institute, CFA. 2015 CFA Level II Volume 5 Alternative Investments and Fixed Income. Wiley Global Finance, 2014-07-14. VitalBook file.

The citation provided is a guideline. Please check each citation for accuracy before use.

In Elan Guides this 2.5% coupon would have been discounted along with the value of the bond in the two nodes. This is what makes sense to me. Why is there a difference and which one is right?

[tickersu]

@SpareTime

In the CFA Curriculum they do not discount the coupon payment when calculating the value of a node. Here is an example, where they are taking the average of the two nodes to the right. However, the 2.5 is outside the bracket and is not discounted by the 1 year node rate, 1.4925%.

Value =0.5 × [(104.0168/1.014925 + 104.6350/1.014925)] + 2.5=0.5 × [102.4872 + 103.0963] + 2.5=105.2917

Institute, CFA. 2015 CFA Level II Volume 5 Alternative Investments and Fixed Income. Wiley Global Finance, 2014-07-14. VitalBook file.

The citation provided is a guideline. Please check each citation for accuracy before use.

In Elan Guides this 2.5% coupon would have been discounted along with the value of the bond in the two nodes. This is what makes sense to me. Why is there a difference and which one is right?

I would go with the CFAI text. Also, think of the timing to help guide you through the example. At a node, you are receiving a coupon, so it is added to the discounted future cash flows, but the coupon itself is already at its present value.

For example (outside the tree approach), if you buy a coupon bond today, you will experience this situation in one period from now. You will receive the coupon, and your bond will be worth the PV of the remaining expected CFs. So at time 1, we add Coupon + (Sum of discounted future CFs) to get a quantity, say V1. If we wanted to bring this entire value back to time 0, we would then discount V1 (which includes the time 1 coupon) to time 0 to give V0.

Hope this helps.

Edit: I’ve reread your post, and now I’m not sure if I understood the question as written. I don’t have the book with me, so I’m going to see if I can find the tree diagram in vitalsource.

Edit to the Edit: I found the tree, and what they’ve done is correct. They’re taking the TIME 2 values of the bond and discounting back to TIME 1 (node 1,2) (weighting them) and adding the coupon to get the total value at time 1, so my example works for this.

[SpareTime]

@tickersu

@SpareTime

In the CFA Curriculum they do not discount the coupon payment when calculating the value of a node. Here is an example, where they are taking the average of the two nodes to the right. However, the 2.5 is outside the bracket and is not discounted by the 1 year node rate, 1.4925%.

Value =0.5 × [(104.0168/1.014925 + 104.6350/1.014925)] + 2.5=0.5 × [102.4872 + 103.0963] + 2.5=105.2917

Institute, CFA. 2015 CFA Level II Volume 5 Alternative Investments and Fixed Income. Wiley Global Finance, 2014-07-14. VitalBook file.

The citation provided is a guideline. Please check each citation for accuracy before use.

In Elan Guides this 2.5% coupon would have been discounted along with the value of the bond in the two nodes. This is what makes sense to me. Why is there a difference and which one is right?

I would go with the CFAI text. Also, think of the timing to help guide you through the example. At a node, you are receiving a coupon, so it is added to the discounted future cash flows, but the coupon itself is already at its present value.

For example (outside the tree approach), if you buy a coupon bond today, you will experience this situation in one period from now. You will receive the coupon, and your bond will be worth the PV of the remaining expected CFs. So at time 1, we add Coupon + (Sum of discounted future CFs) to get a quantity, say V1. If we wanted to bring this entire value back to time 0, we would then discount V1 (which includes the time 1 coupon) to time 0 to give V0.

Hope this helps.

Edit: I’ve reread your post, and now I’m not sure if I understood the question as written. I don’t have the book with me, so I’m going to see if I can find the tree diagram in vitalsource.

Edit to the Edit: I found the tree, and what they’ve done is correct. They’re taking the TIME 2 values of the bond and discounting back to TIME 1 (node 1,2) (weighting them) and adding the coupon to get the total value at time 1, so my example works for this.

Thanks for your help. I see that you’re right, and CFAI way is correct. After reading this I went through the Elan stuff and I did it their way and got the same answer. The only difference was where the coupon was accounted for…Elan did it immediately and then discounted, whereas CFAI discounted first and then added the coupon, but then it still gets discounted in the next step…they end up being the same answer.

[tickersu]

Glad to help! It’s good you reconciled the differences in the approaches. I haven’t looked at the Elan method, but all that matters is getting the correct answer (and hopefully understanding why it is so).