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Valuation of convertible bond based on uncertain fractional differential equation
Convertible bond is a hybrid financial derivative with the properties of debt and equity, which provides the holder with a right to convert bond into the issuer’s stock at a prescribed ratio in the future. This paper analyzes the valuation problems of convertible bond on the basis of uncertain fractional differential equation. Then the prices of convertible bond are obtained by means of expected value criterion and optimistic value criterion, respectively. Besides, numerical examples are given to compare expected value models with optimistic value models. Finally, an empirical study is provided to illustrate that the uncertain fractional stock model is superior to the classical stochastic model.
Journal Article
Valuation of Euro-Convertible Bonds in a Markov-Modulated, Cox–Ingersoll–Ross Economy
This study investigates the valuation of Euro-convertible bonds (ECBs) using a novel Markov-modulated cojump-diffusion (MMCJD) model, which effectively captures the dynamics of stochastic volatility and simultaneous jumps (cojumps) in both the underlying stock prices and foreign exchange (FX) rates. Furthermore, we introduce a Markov-modulated Cox–Ingersoll–Ross (MMCIR) framework to accurately model domestic and foreign instantaneous interest rates within a regime-switching environment. To manage computational complexity, the least-squares Monte Carlo (LSMC) approach is employed for estimating ECB values. Numerical analyses demonstrate that explicitly incorporating stochastic volatilities and cojumps significantly enhances the realism of ECB pricing, underscoring the novelty and contribution of our integrated modeling approach.
Journal Article
The handbook of hybrid securities : convertible bonds, coco bonds, and bail-in
Introducing a revolutionary new quantitative approach to hybrid securities valuation and risk management
To an equity trader they are shares. For the trader at the fixed income desk, they are bonds (after all, they pay coupons, so what's the problem?). They are hybrid securities. Neither equity nor debt, they possess characteristics of both, and carry unique risks that cannot be ignored, but are often woefully misunderstood. The first and only book of its kind, The Handbook of Hybrid Securities dispels the many myths and misconceptions about hybrid securities and arms you with a quantitative, practical approach to dealing with them from a valuation and risk management point of view.
* Describes a unique, quantitative approach to hybrid valuation and risk management that uses new structural and multi-factor models
* Provides strategies for the full range of hybrid asset classes, including convertible bonds, preferreds, trust preferreds, contingent convertibles, bonds labeled \"additional Tier 1,\" and more
* Offers an expert review of current regulatory climate regarding hybrids, globally, and explores likely political developments and their potential impact on the hybrid market
* The most up-to-date, in-depth book on the subject, this is a valuable working resource for traders, analysts and risk managers, and a indispensable reference for regulators
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AN ANALYTICAL APPROXIMATION FOR CONVERTIBLE BONDS
This paper looks at adapting the method of Medvedev and Scaillet for pricing short-term American options to evaluate short-term convertible bonds. However unlike their method, we provide explicit formulae for the coefficients of our series solution. This means that we do not need to solve complicated recursive systems, and can efficiently provide fast solutions. We also compare the method with numerical solutions, and find that it performs extremely well, giving accurate bond prices as well as accurate optimal conversion prices.
Journal Article
Financial Traits and Convertible Bond Motives: China’s Evidence
Convertible bond financing has gained significant traction in China’s capital market, yet it poses financial risks, particularly for highly leveraged firms. This study investigates how corporate financial traits influence the decision to issue convertible bonds, challenging the direct applicability of Western theoretical frameworks in China’s unique institutional context. We employ a natural experiment design, constructing a binary logistic regression model to analyze data from Chinese A-share listed companies that issued convertible bonds, corporate bonds, seasoned equity offerings, or rights offerings between 2022 and 2023. Our results reveal a paradox: contrary to risk-transfer theory, firms with lower leverage exhibit a stronger propensity to issue convertible bonds. Instead, motives are driven by high profitability, operational inefficiencies, and robust operating cash flow generation—traits that align with signaling and backdoor equity theories. The study identifies China’s convertible bond market as a dual-track system where regulatory screening distorts classical motives while market frictions amplify the role of convertible bonds in resolving information asymmetry. We conclude with targeted policy implications for regulators and corporate treasurers to enhance market efficiency and governance.
Journal Article
Contingent Capital Instruments for Large Financial Institutions: A Review of the Literature
As the recent financial crisis unfolded, a new financial instrument—contingent convertible (coco) bonds—was widely considered as a mechanism for promptly recapitalizing overlevered financial institutions. Essentially, the conversion feature of coco bonds would replace supervisory discretion about banks’ capital adequacy with rules specifying when new equity was required. Academics and regulators conjectured that including sufficient cocos in a bank’s capital structure could substantially insulate taxpayers from private investment losses. This potential fostered a literature evaluating the effect of cocos on bank and financial sector stability, risk-taking incentives, and corporate governance. I review this literature and suggest that regulatory capital definitions should be expanded to include substantial amounts of carefully designed coco bonds as a partial substitute for common equity in regulatory capital requirements.
Journal Article
Research on Pricing Methods of Convertible Bonds Based on Deep Learning GAN Models
This paper proposes two data-driven models (including LSTM pricing model, WGAN pricing model) and an improved model of LSM based on GAN to analyze the pricing of convertible bonds. In addition, the LSM model with higher precision in traditional pricing model is selected for comparative study with other pricing models. It is found that the traditional LSM pricing model has a large error in the first-day pricing, and the pricing function needs to be further improved. Among the four pricing models, LSTM pricing model and WGAN pricing model have the best pricing effect. The WGAN pricing model is better than the LSTM pricing model (0.21%), and the LSM improved model (1.17%) is better than the traditional LSM model (2.26%). Applying the generative deep learning model GAN to the pricing of convertible bonds can circumvent the harsh preconditions of assumptions, and significantly improve the pricing effect of the traditional model. The scope of application of each model is different. Therefore, this paper proves the feasibility of the GAN model applied to the pricing of convertible bonds, and enriches the pricing function of derivatives in the financial field.
Journal Article
Contingent Convertible bond literature review: making everything and nothing possible?
Contingent Convertible (CoCo) bonds are subject to a considerable theoretical and practical debate. This article presents a systematic literature survey from five databases between 2002 and June 30, 2018, based on a content analysis approach. I do so by analyzing the multidisciplinary linking points of 244 CoCo-related publications from 27 countries. This literature review considers—in addition to peer-reviewed journal articles—first-tier gray literature in order to receive the most comprehensive picture possible. Although CoCos that qualify for Basel III have various advantages such as less social costs due to optimal capital regulation and equilibrium leverage, lower default risk, cheaper financing and enhanced returns for issuers, they cause at least as many undesirable effects in the field of moral hazard such as the preference for higher risk-taking of management and equity holders or the acceptance of elevated asset volatility as a result of the high wealth transfer risk for CoCo holders. The explanations for the established CoCo design are multifaceted and vary greatly. In academia, caution needs to be exercised on the tendency to over-engineer the possible future design of CoCos and the myriad of outcomes.
Journal Article