Hi,
If we experience a shift in the yield curve. We calculate a new Binominal Tree based on the new rates. But what about the OAS?
Do we also calculate new OAS, or do we simply add back the OAS we had before the change in the term structure?
I remember reading a mock exam solution for Shwesser and it assumed that OAS did not change when there was a parallel shift in interest rates. They simply added the OAS from the initial tree to the new one.
Just calculate the OAS before imposing parallel shifts.
I am sure you are aware of the whole process, but just as a reminder 
Step 1: Given assumptions about benchmark interest rates, interest rate volatility, and the call and/or put rule, calculate the OAS for the issue using the binomial model. Step 2: Impose a small parallel shift in the on-the-run yield curve by an amount equal to +Δy. Step 3: Build a new binomial interest rate tree using the new yield curve. Step 4: Add the OAS to each of the 1-year forward rates in the interest rate tree to get a “modified” tree. (We assume that the OAS does not change when interest rates change.) Step 5: Compute BV+Δy using this modified interest rate tree. Step 6: Repeat steps 2 through 5 using a parallel rate shift of −Δy to estimate a value of BV−Δy.