Trying to understand the meaning of current coupon spread duration? Is this same as empirical mortgage spread duration?
No. The current coupon spread is the excess spread offered by the current coupon mortgage over the reference yield curve. Since the current coupon drives mortgage rates, the idea behind the Current Coupon Spread duration measure is to isolate the impact of changes in primary mortgage rates on MBS prices, assuming that there is no change in the reference yield curve.
On the other hand, the spread (or OAS) duration measures the sensitivity of MBS price changes to changes in the OAS risk premium (all else being equal).
Changes in the current coupon spread impact prepayment speeds and hence MBS cash flows whereas changes in the OAS spread have no impact on MBS cash flows.