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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. [ABSTRACT FROM AUTHOR]

The Convertible Bonds (CBs) market has witnessed an unprecedented level of activity over the last few years not only in developed countries such as the United States but also in BRICK countries such as China. Exploring new properties of CBs or CBs with clauses becomes important for academia communities in financial mathematics. In this paper, we build two coupled partial differential equations (PDEs) for pricing a callable CB, and find a newly identified inherent property of this bond. The new property is that the conversion ratio will not affect the critical recall time indicating the time beyond the callability. Besides this property, we also find that solving the critical recall time separately and superimposing later using a non-callable CB is the same as the method of a hybrid free boundary (the critical recall time) and a moving boundary (the optimal conversion price) though the callability and the American-style conversion are nonlinearly coupled. [ABSTRACT FROM AUTHOR]

Some firms issue mezzanine for future growth, while some others abuse it. Using Korean firms during 2015-2018, we examine the association between convertible bonds (CB) bonds with warrants (BW) issuance and firm value. We find that issuing CB (BW) is positively associated with firm value, and for firms growing fast, the positive association is strengthened, consistent with investment expansion theory. For firms with greater ownership by the largest shareholder and affiliated parties, the positive association is attenuated, consistent with the wealth transfer hypothesis. Moreover, when outside directors attend a board meeting to issue CB, it has a positive association with firm value. [ABSTRACT FROM AUTHOR]

Convertible bond is a compound derivative security involving bond, stock and option. Its pricing has always been one of the hot issues in financial mathematics. In this paper, a variety of stock data were used as samples, the long-term dependence and no-constant volatility of stock price was considered, the stock price model with regime switching was established in the fractional Brownian motion environment, the actuarial method and Monte Carlo simulation algorithm were used to price the convertible bond, the market data of Shanghai Bank Securities and Shanghai Bank convertible bond were used for empirical analysis. The empirical results show that the stock price model with regime switching in fractional Brownian motion environment is more suitable for the actual financial market. [ABSTRACT FROM AUTHOR]

This article investigates whether, when and how firms actively manage media coverage when they plan to issue convertible bonds. Using a sample of listed firms that issued convertible bonds between 2010 and 2020 in China, we find that both firms' media coverage and positive slant increase one month before issuances and active media management has a positive impact on conversion prices. Overall, our results support the active media management hypothesis and verify that firms actively manage media coverage prior to convertible bond issuances. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

While ordinary options are wholly exercised at a chosen time to maximize holders' benefits, empirical evidence favors the intertemporal exercise of corporate securities such as convertible bonds and executive/employee stock options. This is because the exercises of these securities can dilute the issuers' equity, inject capital into the issuers' assets, and change the capital structures, which influences the exercise payoffs and the remaining security values. However, the literature simplifies these impacts on exercise policies, leading to biased and even irrational pricing results. We address this via a state-transition forest that partitions the securities into k units and the time span of the forest into n steps. A representative holder can exercise an integral multiple of units at different steps to maximize her benefit, given that the lump sum of the exercise units does not exceed k. It can be further extended to model intertemporal exercises conducted by competitive investors who hold too-small amounts of securities to influence prices. The forest is then composed of k + 1 trees to capture transitions among capital structures due to different lump sums of option exercise units. The intertemporal exercise decision at each forest node is optimally determined by recursively solving the Bellman equation. This carefully designed forest structure reduces the running time complexity from O (n 2 k) to O (k 2 n 2). We show that ignoring or simplifying intertemporal exercises and corresponding dilutions/injections significantly influences pricing results. [ABSTRACT FROM AUTHOR]

We document frequent occurrences of negative conversion premium (NCP) events in the Chinese convertible bond market, when the bond is convertible and the underlying stock can be freely sold. This implies that when an NCP event occurs, existing stock holders can earn a riskless profit through a long-short strategy which sells the underlying stock and buys the convertible bond at the same time, then converts the bond into stocks. Facing short sale constraints, traders not holding any position in the underlying stock can still profit from an overnight trading strategy which buys the convertible bond at the NCP event day t, then sells the converted stock on day t þ 1. We also find that the next-day opening prices following NCP events are significantly lower, which is evidence for the stock selling from the overnight trading strategy. Overall, our findings show that investors in China are aware of the NCP events and they earn abnormal returns through active trading. However, it remains as a puzzle why existing stock holders such as institutional investors do not trade away the negative conversion premium through the riskless long-short strategy. [ABSTRACT FROM AUTHOR]

Although bonds play an important role in U.S. capital markets, this financial instrument is less common in the emerging markets. Taiwan is a typical case. In fact, both bond issuances and bond transactions in Taiwan have been declining in the past years. Consistent with the previous studies, this research documents that wealth transfer effects exist between bondholders and stockholders. We hypothesize that this wealth transfer discourages investors from investing in bond markets because companies in Taiwan seem to care less about the interest of bondholders. Using the event study methodology, we examine the price change of bonds and stocks in Taiwan capital market around cash dividend announcements. We find that there are significant abnormal returns before cash dividend announcements from 30 days to 60 days and that there is insignificant price change of bonds during the three-day period around the announcement. Possible explanations of the results include low bond trading volumes, insider trading before announcements, and mixing signaling and wealth transfer effects. Although this study cannot prove that the results are directly related to management holdings, we tend to believe that insider trading somehow matters. [ABSTRACT FROM AUTHOR]

To the in conformity that the assumption of constant volatility in the traditional Black Scholes model is not consistent with the real financial market, the G-Brownian motion was used to describe the changes of the stock price and establish the financial market mathematical model. The sliding window method was used to estimate the upper and lower variance, the relevant theories of G-Brownian motion and the definition were used to simulate the underlying asset price. The Monte Carlo method was used to simulate the price of the embedded call option of the convertible bond, and the convertible bond is further priced. The empirical analysis was made through the data of Changzheng convertible bond transactions, and compared with the pricing results of the traditional Black-Scholes model. The results show that the financial market model in the G-Brownian motion environment is more adapted to the real financial market than the traditional Black-Scholes model. [ABSTRACT FROM AUTHOR]

The convertible feature attached to a newly issued bond represents an embedded option whose value is determined by firm. The embedded option's implied volatility reflects the firm's view of its stock price risk which may differ from that of the market reflected in the exchange‐traded option. If such a gap in implied volatilities exists, it may create arbitrage opportunity for investors. Hence, we determined the gap between the implied volatilities extracted from the U.S. exchange‐traded option and embedded option and investigated its potential contributing factors, including corporate variables (price‐to‐book, market capitalization, cost of debt, debt‐to‐equity) and bond variables (maturity, default probability). The result showed that, during 2014–2016, the difference existed and was attributed to the firm's market capitalization. Our finding suggests the potential arbitrage opportunity in the debt, equity, and convertible instruments of small market capitalization firms. [ABSTRACT FROM AUTHOR]

Convertible bond becomes an important way of refinancing for Chinese listed companies recently, and the pricing problem of convertible bond has attracted wide attention. In this paper, we propose a two-factor willow tree method to price Chinese convertible bonds with the consideration of stock price, interest rate, default rate and the trigger conditions of callable and putable clauses embedded in Chinese convertible bonds. By comparing with the existing models, our model matches the market prices better. In empirical research, we estimate the volatility of the stock price process with both historical volatility and implied volatility which is got by calibrating the valuation model with the market price of convertible bond. We find that the accuracy of the valuation model has been greatly improved. [ABSTRACT FROM AUTHOR]

This paper introduces a new class of Dynkin games, where the two players are allowed to make their stopping decisions at a sequence of exogenous Poisson arrival times. The value function and the associated optimal stopping strategy are characterized by the solution of a backward stochastic differential equation. The paper further provides a replication strategy for the game and applies the model to study the optimal conversion and calling strategies of convertible bonds, and their asymptotics when the Poisson intensity goes to infinity. [ABSTRACT FROM AUTHOR]

This paper attempts to identify the determinants of credit ratings for debt instrument issuers in the so-called emerging markets. The study was conducted on the sample of convertible bonds issuers in 2001-2012, half of which originated from Central and Eastern Europe, while the rest were U.S. operators. The analysis is focused exclusively on pairs of bonds with the same rating given by the British Fitch agency, which specialises in analysing Central and East European markets. The conducted studies show that solvency risk, interpreted as indebtedness, financial leverage and current solvency, is a major difference between the two groups of bonds. Changes in indebtedness, i.e. in assets held by foreign investors, are apparently the reasons of higher requirements for issuers from the emerging markets.