A Basic question I thinkSay I have a bond which can default and I know the yield to maturity on the bond, the risk free rate and the recovery rate (hence I know the risk free default probability) and coupon rate and the maturity date of the bond....From this info how can I get the price of the bond today? In particular do I have to use information about the default probability to price the bond or is all this information contained in the y.t.m??

ok so you do use risk neutral probability info to price it

Can someone please check this5 year corporate zero which has a flat yield of 9.11% over the five years..The risk free rate is 5%..Recovery rate is 0.4 of face value and if defaults occur they occur payoff ocurrs at the end of the year..Hence if a default occurs in the period 0-1 years you will get the payoff 0.4 at time t1=12 months..If default occurs in the period 1-2..payoff will be at 24 months etcThe price I get using these assumptions is approx 0.64. Can someone please check it??

anyone?

You would also need Par CDS spreads, no?

why??Can i not just get a good proxy for default prob using this alone...

I still do not understand your question. Suppose the default probability is 100% in year 1, the price then should be a discounted 0.4, right? In general, depending on default probs, you would get different prices.And how can you get the default probs, if you do not know the price of the bond?

see hull

I would have thought that all the default information is incorporated in the 'yield' as you pointed out.In fact, you should be able to use the yield data to work out what the default probability is (assuming an intensiy model for deafult)...I agree with the 0.64 answer; seems rational.Regards,

I suppose that the yield is all you need to get the price of the bond, since it encodes all the information. (risk free rate, spread, recovery rate, and probability of default).You can use the yield to get the price of the bond, and then you can implement a model (let's say an intensity model) that uses risk-free, recovery rate, probability of default to find the implied probability of default (which is the only thing you dont know/assume).You can also use a model with risk-free rate and spread only, and find the implied spread (which includes the recovery rate) from the yield and the risk free rate, etc.

The main problem with this is you don't know the recovery rate until after the bond defaults, you're just guessing, and so guessing at the price

That's true, but a recovery rate of 0.4 is a standard assumption.

Like the BS vol, the yield of a bond is just a number that you plug into a formula to get back the bond price. Your pricing therefore depends on the assumptions used in deriving that yield. If the possibility of default was incorporated then you should be able to just use this number as you would use the yield of, say, a government bond. If the possibility of default wasn't incorporated you could construct the risk-free discount factors using that yield and the survival probabilities etc. using the CDS spreads for the bond issuer and proceed much the same way you would when valuing a credit-linked note. In your example, because the bond yield is so much higher than the risk-free rate it's possible that the credit spreads have already been taken into account when deriving the yield.