Real world PD vs. risk-neutral PD (Hull 23.19)

[RiskNoob]

Hi David, BT folks,

I am having a bit of trouble understanding default probabilities in two different worlds. My intuition is that real world default probabilities should be `more` than risk-neutral default probabilities due to the CAPM framework (e.g. people usually takes more risk (hence more PD) for more return in the real world, as opposed to the risk-neutral world, where people takes the expected rate which is risk-free, hence less PD than the real world).

Or should I be think in the opposite way - simply because the risk-neutral default probability is a `conservative` approach. This makes sense to me but I can`t express the reasoning in the formal (say from FRM perspective) way.

Any tips would be helpful,

Thanks,

RiskNoob



Quote from PQ:

23.19. Does valuing a credit default swap (CDS) using real-world default probabilities rather than risk-neutral default probabilities overstate or understate its value? Explain your answer.

Answer:
Real world default probabilities are less than risk-neutral default probabilities. It follows that the use of actuarial default probabilities will tend to understate the value of a CDS.

 

[Mark W]

Well, an off the top of my head answer would be that risk neutral probabilities => no arbitrage and make expected discounted value match market prices ~ factors in uncertainty so default probabilities would be higher due to this. Perhaps worth going back to the Tuckman binomial tree stuff in T5, unfortunately I don't have it with me at present.

Thanks