A stochastic‐volatility equity‐price tree for pricing convertible bonds with endogenous firm values and default risks determined by the first‐passage default model

This paper proposes a novel equity‐price‐tree‐based convertible bond (CB) pricing model based on the first‐passage default model under stochastic interest rates. By regarding equity values as down‐and‐out call options on firm values (FVs), at each tree node, we solve the implied FV and equity‐price volatility (EPV), and then endogenously settle the default probability (DP) and also the dilution effect subject to CB conversions with the implied FV and capital structure. Our model captures the stylized negative (positive) relationships between the stochastically evolving DP and FV or EP (EPV) that cannot be fully achieved by existing CB pricing models.