Backward Induction

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borson

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Hey all, currently working through the fixed income chapter (still waiting for Wiley Guides to release their practice questions) and i’ve become a bit confused by some conflicting methods with backwards induction.
A good example is in Reading 43, example 3: Pricing a Bond Using a Binomial Tree
The formula given right above is denoted as .5x{[(VH+C)/(1+i)]+[(VL+C)/(1+i)]} however in the example right below it seems to use a different formula given as .5x{[VH/(1+i)]+[VL/(1+i)]}+C
Maybe it’s just late and I can’t do the math right now but I get a different value with the two different formulas. I’m assuming this means I am supposed to use the different variation for different situations but I can’t work out what that is.
Would anyone be able to shed some light on this form me? It would be greatly appreciated.
Kind Regards,
Borson
 
Thanks,
I only get slightly different values between the two formulas, must be due to rounding. Thank you very much for clarifying.
Kind Regards,
Borson
 
borson wrote:still waiting for Wiley Guides to release their practice questions
Click to expand...
I was looking at purchasing some practice questions. Which sections have Wiley released and which ones still have yet to be?
 
HI Borson,
Algebrailically they are different.
5x{[(VH+C)/(1+i)]+[(VL+C)/(1+i)]}
This works out the intinsic value of the bond at a particular node which you are working out
5x{[VH/(1+i)]+[VL/(1+i)]}+C
This workds out the entire value of the bond at a particular node, which is the discounted entire value from a subsequent node plus the coupon that was given to you at that particular point in time.
That is why you will notice that when you use the second equation to calculate your bond value at V0, ie you work backwards until you get to the start , equation2 is identical to equation 1 because at time 0, there is no coupon when you work out the ENTIRE value, so C=0 and 5x{[VH/(1+i)]+[VL/(1+i)]}+C=5x{[VH/(1+i)]+[VL/(1+i)]}+0
Hope this helps as i also had an issue trying to figure out the difference between the 2.
 
I answered too hastily, and, thanks to that, was wrong.
Thanks for keeping me honest, mohamedsaif!
In the first you’re discounting the coupon by (1 + i), and in the second you’re not.
I’ll crawl back into my hole now.
 
Interesting, so i’m not as dumb as I thought!
Thank you for clarifying.
However that leads me back to being confused as to when to use each formula. Is there an appropriate situation where one formula is used vs the other formula? I’m comfortable using either formula and remembering them both, but I currently can’t understand when to use one vs the other.
Kind Regards,
Borson
 
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