Hi All,
I've done a lot of reading on the forum as well as externally trying to bog down this concept. (Special thanks to Mark and Mugono's threads that helped tremendously). I think I'm almost settled but I wanted to clarify my understanding.
So one way the market consistent approach was explained (IMO) is the concept of the risks that the liability is supposed to be exposed to. So for an insurance liability, that would include lapse, mortality, expenses (?) but it would not include market risk because from the p/h's perspective, they are paying for mitigation agst mort, lapse (non hedgeable). Said another way, since $100 of a bond and $100 of a stock both provide $100, the liability value won't change based on what asset is chosen so there's no market related risk. So both are looked at the same way. As such, market risk should not be included in the discount rate. Is this correct?
The second approach is the one from the notes where it speaks to a replicating portfolio concept. I took CT8 many MANY years ago so I'm a bit rusty but basically I accept the replicating portfolio concept and that risk-free rates are req'd in the use of a market consistent valuation. So if a risk free ZCB can replicate an annuity liability then they should both have the same value. I guess my hang up is why use a risk-free ZCB? We could have also used a risky ZCB to replicate the liab. CFs but then the liab would not use the risk-free rate (it would use the rate associated with the risky ZCB). Is it because of the concept of requiring risk-free rates for a market consistent valuation? I feel my logic is becoming a bit circular so some help would be appreciated.
Thanks much!
I've done a lot of reading on the forum as well as externally trying to bog down this concept. (Special thanks to Mark and Mugono's threads that helped tremendously). I think I'm almost settled but I wanted to clarify my understanding.
So one way the market consistent approach was explained (IMO) is the concept of the risks that the liability is supposed to be exposed to. So for an insurance liability, that would include lapse, mortality, expenses (?) but it would not include market risk because from the p/h's perspective, they are paying for mitigation agst mort, lapse (non hedgeable). Said another way, since $100 of a bond and $100 of a stock both provide $100, the liability value won't change based on what asset is chosen so there's no market related risk. So both are looked at the same way. As such, market risk should not be included in the discount rate. Is this correct?
The second approach is the one from the notes where it speaks to a replicating portfolio concept. I took CT8 many MANY years ago so I'm a bit rusty but basically I accept the replicating portfolio concept and that risk-free rates are req'd in the use of a market consistent valuation. So if a risk free ZCB can replicate an annuity liability then they should both have the same value. I guess my hang up is why use a risk-free ZCB? We could have also used a risky ZCB to replicate the liab. CFs but then the liab would not use the risk-free rate (it would use the rate associated with the risky ZCB). Is it because of the concept of requiring risk-free rates for a market consistent valuation? I feel my logic is becoming a bit circular so some help would be appreciated.
Thanks much!