We have a pair of simultaneous equations that can be solved for V0 and s V . Having found V0 and sigmaV we can then find the value of the corporate debt allowing for the possibility of default. In addition, F(-d2 ) gives us an estimate of the risk-neutral probability of default. Would you plz explain this. Are the 2 eqns are the Black-Scholes formula and the one obtained using Ito's lemma? We need to find V0 from this and the D = V0 - E0. Is that it?
Yes, these are the equations you mentioned. Value of bond (D) = V0 - E0, this seems to me as value of bond allowing for the possibility of default. If we compare this value of bond with risk-free bond then the difference between risk-free and D might give us price of credit derivative. I am not sure but this is my understanding.
The difference between the corporate bond and the risk free bond is the Expected present value of the credit loss over the life of the bond. With additional input of Loss Given Default, this value can be used to calculate the probability of default. Alternatively we can use this to calculate the CDS spread.
So can we say this expected present value of credit loss is the price of CDS? And what is the CDS spread you are referring to? The spread over risk free rate?
CDS spread is the regular payments protection buyer pays to the protection seller over the life of the swap. In return should the reference entity default, the protection buyer receives the loss given default as payout. One can calculate the swap spread by equating the EPV of credit loss with EPV of swap payments. For this we need unconditional pd, discount factors, loss given default and assumptions abt timing of default. There are worked examples given in the Hull's book.
