Error bounds and convergence for American‑style convertible bonds

Develop rigorous error estimates and convergence proofs for the CTMC‑based optimal stopping algorithm proposed for pricing American‑style convertible bonds with stochastic interest rates and credit risk using the Tsiveriotis–Fernandes split.

Background

The paper introduces a CTMC optimal stopping algorithm for American‑style convertible bonds and provides extensive numerical evidence of accuracy and efficiency. However, due to payoff discontinuities arising from different discounting for equity and debt components, a complete convergence theory is not provided.

The authors explicitly state that a detailed error and convergence analysis for this American‑style convertible bond setup remains to be done.