In Hull 23, to calculate the default probability of a bond, we're told to equate the price impact of risk with the expected value of losses given a default. The price impact of risk is intuitive; price the bond using both the risk free rate and the yield and the difference is the price impact of risk.
What I'm having trouble grasping is why we use the risk free rate to price the "Loss Given Default" values. I interpret "Loss Given Default" as a bond's current value minus any recoveries. This to me would be calculated by discounting any future cash flows at the yield of the bond, then subtracting the expected recovery.
However, in the CAS solutions, they use the risk free rate to discount future cash flows which doesn't make sense to me. Wouldn't we be calculating the price of a risk free bond in that case?
What I'm having trouble grasping is why we use the risk free rate to price the "Loss Given Default" values. I interpret "Loss Given Default" as a bond's current value minus any recoveries. This to me would be calculated by discounting any future cash flows at the yield of the bond, then subtracting the expected recovery.
However, in the CAS solutions, they use the risk free rate to discount future cash flows which doesn't make sense to me. Wouldn't we be calculating the price of a risk free bond in that case?
Loss Given Default
