# Valuing Bonds

Hello, I started to study with fixed income… But I get stuck in the reading 54 with the binomial model. Serious posted a Q about this, but I just dont get it. I understand that I have to do some Backward induction calculation, but I don’t know from where to where. Can someone tell me what we should know how to do whit these problems? Maybe Knowing how to calculate some values with the volatility… Maybe some average calculations… Please, for you who knows how to do all these kind of solving problems perfectly, could you tell me how to do the approach to it or how to look at it??? As example… What they do in practice Question 1 pg. 307 book5? Thanks

i have not gotten the books yet, but in order to solve the problems you start with the maturity year and work backwards starting with the par value. You then add the coupon to the par value and divide by 1+i which should be showing up in the box. The i is value that is generally based on an some volatility model but isnt important when for the test. When you are dealing with combining 2 nodes you simply calculate for each i and average the two. Example if you are trying to value a bond that matures for \$1000 and it pays an annual coupon of \$60 you add it to par to get \$1060. Now you divide the 1060 by the interest rate the is given in the last box, let’s say 5%. You get a value of \$1009.52. Now say the next i in the box below is 7% you get 1060/1.07 you get \$990.65. Intuitively this should make sense because if rates jump to 7% your bond paying 6% should fall in price, and the opposite should happen if rates fall to 5%. In order to find the value to plug into the node to the left you then average 1009.52+990.65/2 gives you 1000.085. Then to get the next one over you divide 1000.085 plus the 60 coupon by whatever i is given in that box

Thanks a lot. YOU ARE THE MAN!

No problem, and one more thing, if the bonds have an embedded option you must adjust for that in your calc. For example, if its callable and rates drop to the point that gives you a value greater than par you simply use the par value instead of the calc value because you assume that since rates dropped the bond will be called so in the above example when rates dropped to 5% you would not use the \$1009 simply use the par

got it. But, is there any relation between the rHH rate to discount in i.e.: year 2 an the rate rHHH in year 3? Ok about relation rHHH and rHHL (which is the volatility, the rHHL=rHHH * e^2*Vol.) but dont ger where the firs r cmes from…

Not sure exactly what you are asking by the first r, but if i remember correctly the first r in the tree I believe is the current benchmark rate, i would have to double check the book and will do so, but if you could clarify your question a little more it might help. sorry bud, keep me posted.

yes I think it is the benchmark rate, so from there to the next years higher rate? what is the relation?

The relationship would be based on the assumption that from current r the rate increases/decreases in time t+1. How the higher and lower numbers are arrived are based on some volatility calculation that a given program uses, but for the exam we don’t have to know where the new rates come from, just how to use them to derive the price

I love bonds

I_Passed_Level_1 Wrote: ------------------------------------------------------- > I love bonds hahaha Its crazy we are crazy … BUT Getmackinlyland, somewhere in the book they tell us how to calculate from a rHH to rHL… it is strange. Why they dont say how to go from rH to rHH…

yeah who knows