Bonds with optional sinking feature have already been discussed in the XAIA homepage article “Z-spreads for bonds with optional sinking feature: a Bellman exercise”. However, only in a rudimentary stochastic framework. Such instruments equip their issuer with the option (but not the obligation) to redeem parts of the notional prior to maturity, therefore the future cash flows are random. In a (non-rudimentary) one-factor model for the issuer's default intensity we show that the pricing algorithm can be formulated and solved as a so-called Markov Decision Process, which is both accurate and quick. The method is demonstrated using a 1.5-factor credit-equity model which defines the default intensity in a reciprocal relationship to the issuer's stock price process.
It is explained how to compute a Z-spread for bonds with optional sinking feature. Such instruments equip their issuer with an option (but not an obligation) to redeem parts of the nominal before maturity; therefore the future cash flows generated by the bond are random. The proposed method coincides with the so-called “worst-ansatz“ in the special case of a callable bond. In the general case it relies on a dynamic programming technique based on the Bellman principle.