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2013 April Q10

D

Darragh Kelly

Ton up Member
Hi,

Just a question regarding the risk-neutral probabilities for the 2 state model.

How can we say that Q1, risk-neutral prob of no default for bond 1 maturing at time 1, is the same for bond 2 which matures at time 2? Is it always the case if the bonds have been issued from the same company regardless of their maturity date then their risk-neutral probabilities of default for each year are the same? eg if there was bond 3 maturing at time 3, prob of no default for bond 3 at time 3 is Q1*Q2*Q3?

Thanks,

Darragh
 
The two-state model says that bonds from an issuer exist under an intensity of default lambda. So in this question Bond 1 and Bond 2 have to endure the same default intensity for one year. If Bond 2 survives then it experiences (potentially) a different intensity of default over the final year.
The risk-neutral probabilities are the fictional quantities required such that the bonds are expected to grow like the risk-free rate. The product of probabilities you've suggested would not apply (I don't think it doesn't apply to Bond 2 either).
 
Yeah all clear on bonds with different maturities having same intensities if issued from same firm thanks for that.

Just lastly on the product of the risk-neutral probabilities, I was saying if there was bond 3 (which expired in 3 years) surely it would experience the same intensity of default as bond 1 and 2 for year 1 and then year 2 bond 2 and 3 would share the same default intensity (which may be potentially different to year 1 as you said)?

Thank you,

Darragh
 
Darragh Kelly said:
I was saying if there was bond 3 (which expired in 3 years) surely it would experience the same intensity of default as bond 1 and 2 for year 1 and then year 2 bond 2 and 3 would share the same default intensity
Click to expand...
Yes, I agree with this. Maybe I misunderstood what "Q1*Q2*Q3" meant :)
 
Darragh Kelly said:
Yeah all clear on bonds with different maturities having same intensities if issued from same firm thanks for that.
Click to expand...
If the bonds have different recovery rates in this question, then they would not have the same transition intensities?

So if they were different would we just calculate it as:

exp(-lambda*2)= No default risk neutral probability (value of 0.76209)
lambda = -0.5*ln(0.76209)
 
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