A stochastic‐volatility equity‐price tree for pricing convertible bonds with endogenous firm values and default risks determined by the first‐passage default model. Issue 12 (8th August 2022)

• Record Type: Journal Article
• Authors: Dai, Tian‐Shyr; Fan, Chen‐Chiang; Liu, Liang‐Chih; Wang, Chuan‐Ju; Wang, Jr‐Yan
• Is Part Of: Journal of futures markets. Volume 42:Issue 12(2022)
• Page Start: 2103
• Page End: 2134
• Publication Date: 2022-08-08
• Subjects: convertible bond -- dilution effect -- first‐passage default model -- stochastic interest rate -- stochastic volatility; Commodity exchanges -- Periodicals; Foreign exchange futures -- Periodicals; 332.632
• DOI: 10.1002/fut.22370
• Languages: English
• ISSNs: 0270-7314

Abstract

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.