# Basic question about bonds pricing

I decided to recap my knowledge in interest rates, and decided to start with Chapter 4 on interest rates (in 8th edition) of the Hull's book "Options, Futures and Other derivatives". In 4.3 the concept of a zero-coupon rate is briefly introduced, and is further used to price a coupon-bearing bond in 4.4. Procedure is natural, logical and relies on clear arbitrage-avoiding arguments. However, in 4.5 zero-coupon rates are themselves computed via the coupon-bearing bond prices. This line feels cyclic to me. I can understand that one can use this to check the consistency of bond prices over several maturities, but does it mean that one can actually price bonds using such arguments?

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Generally, there are few or no zero-coupon instruments traded in the market, especially for longer maturities. However, pricing of many derivatives relies on having a zero curve, so it becomes necessary to construct one using available instruments.

Aside from derivatives, one can use a zero curve fitted to liquid bonds to price new or less liquid issues.

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Thanks Brian, just want to be sure I got you correctly. The price of more liquid bonds is mostly determined by supply/demand arguments, whereas for less liquid bonds one can do pricing based on more liquid issues: the latter can allow for the arbitrage in case the price of the former is inconsistent? – Ilya Sep 27 '13 at 14:21
Exactly. (Sometimes corporate zero curves get "copied" over to new issues from related companies also, but this has mostly been done with CDS spreads as CDS have risen in prominence) – Brian B Sep 27 '13 at 17:43
Very nice, I think that's the answer I was looking for. – Ilya Sep 28 '13 at 11:59

Yea, I just started work at a fixed income shop. We accrete the value of zero coupon bonds based on the coupon rate the bond would have paid if it were an interest/bullet bond. The value of the coupon/accreted rate in the Official statement/indenture of the bond is obviously not the rate the market is pricing the bonds at but it fluctuates around it, assuming the obligor's credit worthiness is not impaired and there is liquidty in the market, otherwise you would have large credit, liquidity premiums. Just think of the accretated rate as a glide path that gets you from the value of the bond now to the par amount at maturity and that the market price/yield, which is different, will fluctuate around this accreted rate all the way up to par.

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I see your point: I just wondered what was the chicken and what was the egg in Hull's case. – Ilya Sep 27 '13 at 14:23