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
