Explain how to apply the arbitrage-free approach when valuing a bond that contains embedded options

To value a bond with embedded options, use a binomial tree calibrated to the benchmark curve with an assumed volatility, and value backward from maturity. At each node where the option can be exercised, apply the exercise rule after computing the continuation value, then add the coupon and continue. For a callable bond, the node value is V = the lower of the computed value and the call price, because the issuer calls when the bond is worth more. For a putable bond, it is V = the higher of the computed value and the put price, because the holder puts when the bond is worth less. Apply the rule at every exercise date, not only the last. For risky issuers, add a constant spread, the OAS, to each node rate.