A stochastic‐volatility equity‐price tree for pricing convertible bonds with endogenous firm values and default risks determined by the first‐passage default model
提出一种基于随机利率下首次通过违约模型的股权价格树方法，通过将股权视为企业价值的向下敲出看涨期权，在每个节点求解隐含企业价值和股权价格波动率，内生处理违约概率和稀释效应，捕捉了现有模型未能完全实现的随机违约概率与企业价值或股权价格之间的负（正）关系。
Abstract 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.