The steps to calculate duration of a callable bond.
- Given assumptions about benchmark interest rates, interest rate volatility, and call or put rule, calculate OAS using binomial model.
- Impose a small shift in the on-the-run yield curve +Δy
- Build a new binomial tree using the new yield curve
- Add OAS to each 1-year forward rate to get a “modified” tree.
- Compute BV+Δy using modified tree
- Repeat steps 2 through 5 using a parallel rate shift of -Δy to estimate value of BV-Δy