Convergence analysis for European‑style convertible bonds

Develop rigorous error bounds and convergence rates for the CTMC approximation of European‑style convertible bonds under bi‑dimensional time‑inhomogeneous stochastic interest rate models that jointly model equity and short‑rate dynamics.

Background

The paper provides a closed‑form matrix expression for European‑style convertible bond pricing via a two‑layer CTMC method and demonstrates empirical accuracy, but comprehensive theoretical convergence for this specific setting has not yet been established.

Existing convergence analyses for two‑dimensional CTMCs focus on stochastic local volatility models rather than stochastic interest rate models. Extending these analyses to the European‑style convertible bond framework is identified as an open task.