Binomial Interest Rate Tree Calcs

CFA Level II
#1

Can some one help me understand why there is a difference in the methods for using the interest rate tree in the CFA practice questions for the fixed income question “Desna” and “Krishnan”? They both have an binomial interest rate tree question, Desna has no embeded option Krishnan does have a put at 98.

The Desna solution does this:

Vuu= 0.5*[102.8/1.0456+102.8/1.0456]+2.8 = 101.117

Vdu,ud= 0.5*[102.8/1.0345+102.8/1.0345]+2.8 = 102.172

Vu=0.5*[101.117/1.0285+102.172/1.0285]+2.8=101.628

For Krishnan:

Vuu= 103.20/1.0621=97.166 (98 Put would be excersided)

Vdu,ud= 103.20/1.0460= 98.662

Vu= 0.5*[98+3.2/1.0431+98.662+3.2/1.0431]=97.336 (bond is put at 98)

My question is why are the coupons treated differently in each example for this? Is this just a you do this when it has an option and you do that when it doesn’t? If any more clarification is needed let me know.

Thanks

#2

I can only suspect the reason lies in the rates used. In Krishnan, the model is calibrated “using yields on par bonds”, while in Desna the rates are forward rates, so no need to discount coupons???

This is still a grey are to me as well. I will have to ask Ioannis Georgiou CFA next time I see him…

#3

Will you be asking him prior to June 4? :slight_smile:

#4

Not really :slight_smile: I was merely showcasing my personal acquaintance with one of the L2 curriculum authors. I can’t really stop him in a social gathering to ask him stupid questions.

What I will do is revisit this topic one of these days. It is in my notes to scrutinize the binomial tree from scratch as I always feel insecure when ecountering such questions. The problem is lack of industry experience in these topics that’s why they are always elusive. Stay tuned to updates.

#5

http://www.analystforum.com/forums/cfa-forums/cfa-level-ii-forum/91350557

#6

I wrote a series of articles on binomial interest rate trees that may be of some help, starting here: http://www.financialexamhelp123.com/binomial-trees-for-fixed-income/

Full disclosure: as of 4/25 I’ve installed the subscription software on my website, so there’s a charge for viewing the articles.

#7

The methods are actually the same. In both instances you take the PV of remaining CF and then adjust for the put/call rules, then take the average of the two, then add the coupon to find the value at that node.

Vu= 0.5*[98+3.2/1.0431+98.662+3.2/1.0431]=97.336 (bond is put at 98) - In this node the average values from Vuu = 98 (the bond was put at this node) +3.2 = 101.2 and the average value for Vul = 98.662+3.2 = 101.862. Then you take the PV of these two values, adjust for the put call rule, then take the average of these two PV’s and add in the coupon to get the value of the bond at that node.

Make sense???