The pricing of perpetual convertible bond with credit risk

Convertible bond gives holder the right to choose a conversion strategy to maximize the bond value, and issuer also has the right to minimize the bond value in order to maximize equity value. When there is default occurring, conversion and calling strategies are invalid. In the framework of reduced form model, we reduce the price of convertible bond to variational inequalities, and the coefficients of variational inequalities are unbounded at the original point. Then the existence and uniqueness of variational inequality are proven. Finally, we prove that the conversion area, the calling area and the holding area are connected subsets of the state space.

The Pricing of Convertible Bonds with a Call Provision

This paper deals with the pricing of convertible bond with call provision based on the traditional B-S formula. By applying the principle of no arbitrage, the partial differential equation for the bond is established with identified boundary conditions, which solution results in the closed form of the pricing formula.

Pricing permanent convertible bonds in EVG model

By considering the failure of normal distribution and continuous assumption in financial modeling, this paper attempts to apply the Exponential Variance Gamma （EVG） model into the pricing framework of permanent convertible bonds with call clause. Following framework of Gapeev ＆ Kiihn（2005）, we obtain an explicit solution to the bond price and optimal stopping strategies, which shows that the new pricing framework is quite different from the continuous model and even the Jump Diffusion model. Compared with the numerical calculation, the closed form results price convertible bonds quickly and accurately.

DeepPricing:pricing convertible bonds based on financial time-series generative adversarial networks

Convertible bonds are an important segment of the corporate bond market,however,as hybrid instruments,convertible bonds are difficult to value because they depend on variables related to the underlying stock,the fixed-income part,and the interaction between these components.Besides,embedded options,such as conversion,call,and put provisions are often restricted to certain periods,may vary over time,and are subject to additional path-dependent features of the state variables.Moreover,the most challenging problem in convertible bond valuation is the underlying stock return process modeling as it retains various complex statistical properties.In this paper,we propose DeepPricing,a novel data-driven convertible bonds pricing model,which is inspired by the recent success of generative adversarial networks(GAN),to address the above challenges.The method introduces a new financial time-series generative adversarial networks(FinGAN),which is able to reproduce risk-neutral stock return process that retains the unique statistical properties such as the fat-tailed distributions,the long-range dependence,and the asymmetry structure etc.,and then transit to its risk-neutral distribution.Thus it is more flexible and accurate to capture the dynamics of the underlying stock return process and keep the rich set of real-world convertible bond specifications compared with previous model-driven models.The experiments on the Chinese convertible bond market demonstrate the effectiveness of DeepPricing model.Compared with the convertible bond market prices,our model has a better convertible bonds pricing performance than both model-driven models,i.e.Black-Scholes,the constant elasticity of variance,GARCH,and the state-of-the-art GAN-based models,i.e.FinGAN-MLP,FinGAN-LSTM.Moreover,our model has a better fitting capacity for higher-volatility convertible bonds and the overall convertible bond market implied volatility smirk,especially for equity-liked convertible bonds,convertible bonds trading in the bull market,and out-of-the-money convertible bonds.Furthermore,the Long-Short and Long-Only investment strategies based on our model earn a significant annualized return with 41.16%and 31.06%,respectively,for the equally-weighted portfolio during the sample period.

Empirical Study on Premiums of Chinese Convertible Bonds

Through analyzing the components of convertible bond＇s value, this paper studied the determinants of premiums of Chinese CBs. According to this research, the premiums in fixed period are significantly higher than that in conversion period due to legal constraints. The premiums in conversion period are negatively related to conversion value, risk-free interest rate, whether the issuing firm has right to advance repayment, whether in selling back period, and additional selling back price, and are positively related to exercise price, risk, and redemption price.

Research on the Pricing of Convertible bonds in China Migration risk based on credit rating

At present,further research and exploration on credit risks are being carried out in the global field,and increasingly profound modem credit risks are exposed to the bond market.This requires that we cannot ignore the impact of credit rating migration risk on bond pricing,so as to adapt to the sustainable and healthy development of the bond market under the new normal of China's economy.The innovation point of this paper is to try to analyze the pricing of Convertible bonds in China from the perspective of credit rating migration risk.Tsiveriotis and Femandes(1998)model is selected,and the credit risk in the model is assumed to be caused by the credit rating migration risk,and the credit spread is used to measure the credit rating migration risk.The research conclusion of this paper is as follows:First,it is valid to consider the risk of credit rating migration in the TF(1998)model.The market price of convertible bonds is on average 1.22% higher 1han the theoretical value of the model.In general,the theoretical value obtained from the model has little deviation from the market price,and has a good fitting degree.Second,from the Angle of credit rating,the selection of 32 samples of convertible bonds only empirical research shows that the credit rating of AA-convertible bonds average deviation rate is negative,suggest that the credit rating of AA-the phenomenon of convertible bonds value is underestimated,and AAA credit rating to AA,AA+,the average deviation rate of convertible bonds is positive,that credit rating AA(containing AA)more convertible bond value is overrated phenomenon,and the higher the credit rating of the average deviation rate of convertible bond,the greater the overvalued levels.It has certain guiding significance for participants in the convertible bond market.

Effect of Issuing Convertible Bonds from the Perspective of Ownership Structure:Evidence from Listed Companies in Shanghai and Shenzhen

Due to the rapid expansion of enterprise scale,traditional financing methods can no longer meet the needs of enterprises.As a financing method with both equity and debt,convertible bonds,with its flexibility,is favored by enterprises.Especially in 2017,China’s supervision on the financing method of private placement of shares has become stricter,and some companies have chosen convertible bonds for financing.This paper takes the ownership structure as the starting point and the listed companies in Shanghai and Shenzhen as the research subjects,as well as uses regression analysis to determine the relationship between convertible bonds,ownership structure,and enterprise performance.It is found that convertible bonds reduce the performance of enterprises,while ownership concentration strengthens the negative relationship.

Empirical Analysis of Impact of Conversion ofConvertible Bonds on Corporate Performance of Different Industries in China

We apply the methods of principle component analysis (PCA) and Wilcoxon’s signed rank test (WSRT) to study influence of conversion of convertible bonds on corporate performance of different industries in China. In this paper, 33 convertible bonds that were issued by non-financial sectors from 2002 to 2009 in China with the convertible rate more than 50% within a year were selected as a research sample. In order to provide a reference for the parties concerned, the influence of conversion of convertible bonds on corporate performance in different industries was studied from the industrial properties point of review.

Convertible Bond Pricing Based on Exponential Variance Gamma Model

Due to the‘spike and tail’ phenomenon of asset returns,the applicability of the Black-Scholes model for pricing convertible bonds has been questioned,and the variance gamma model can cope well with this phenomenon and solve the ‘volatility smile dilemma’.This paper combines the variance gamma model with the least squares Monte Carlo simulation method to empirically analyze the Everbright convertible bond based on its high activity in the Chinese market.In this paper,the predicted price and the actual price are compared,and the applicability of the variance gamma model in the Chinese convertible bond market is analyzed.Empirical results show that the fitting price predicted by the variance gamma model is consistent with the actual price trend,indicating that the method is applicable to the Chinese convertible bond market.

The Valuation of Convertible Bonds with Numeraire Changes

The changes of numeraire can be used as a very powerful mean in pricing contingent claims in the context of a complete market. We apply the method of nurmeraire changes to evaluate convertible bonds when the instantaneous growth and variance of the value of issuer and those of zero-coupon bonds follow a general adapted stochastic process in this paper. A closed-form solution is derived when the instantaneous growth and variance of the value of issuer and those of zero-coupon bonds are deterministic function of time. We also consider a special case when the asset price follows GBM （Geometric Brownian Motion） and interest rate follows Vasicek＇s model.

PRICING CONVERTIBLE BONDS AND CHANGE OF PROBABILITY MEASURE

The changes of numeraire can be used as a very powerful tool in pricing contingent claims in the context of a complete market.By using the method of numeraire changes to evaluate convertible bonds when the value of firm,and those of zero-coupon bonds follow general adapted stochastic processes in this paper,using Ito theorem and Gisanov theorem.A closed-form solution is derived under the stochastic volatility by using fast Fourier transforms.

Binomial Tree Pricing Model of Convertible Bond with Default Risk

In this paper we use a binomial tree to price convertible bond with default risk. A new way about pricing convertible bonds is proposed, which belongs to the deduced form approach. Firstly an inhomogeneous Possion process is used to describe default event and definition of default time. Secondly we combine the stock binomial tree with default intensity and obtain a new tree, then convertible bonds are priced according to the combined tree. It is worth pointing out that the model have following characters： simple, intuitive and having the strong ability to combine other items in convertible bonds＇ indenture.

可转换债券发行及转股对企业运营能力影响的研究——基于我国上市企业的微观数据

2017年再融资新规颁布后,发行可转换债券成为企业融资选择的主要方式之一。依据2010—2020年我国企业可转债发行并转股的相关数据,运用倾向得分匹配和双重差分法研究可转换债券发行及转股对企业运营能力的影响。主要结论为:企业发行可转换债券在短期内会有助于提高企业的偿债能力和投资者财富收入预期,而对经营绩效影响不明显;企业可转换债券成功转股提升企业的经营绩效和投资者对转股后的财富收入预期,降低了企业的杠杆率;可转债发行对国有企业与民营企业经营绩效影响不同,且国有企业在可转债转股成功后杠杆率降低的效果不如民营企业明显。

次分数随机波动率下可转换债券定价

可转换债券作为同时涉及债券、股票和期权的复合衍生证券,其定价是金融数学的热点问题.考虑实际金融资产收益率不具有独立增量和平稳增量,以及波动率具有随机性,建立标的资产价格服从次分数布朗运动驱动的随机微分方程和Hull-White随机波动率模型,采用极大似然估计方法得到模型参数,利用蒙特卡洛法模拟计算可转换债券的价格.结合东时转债实际交易数据进行实证分析,并与其他模型进行对比,结果表明次分数随机波动率下可转换债券定价模型比传统模型更符合金融市场的变化.

科技型中小企业可转债定价模型研究

科技型中小企业具有研发周期长、未来盈利不确定性高、无形资产占比大等特点,随之而来的融资难、融资贵问题严重阻碍了企业的良性发展。可转债融资模式能够充分考虑企业的期权价值,有效改善科技型中小企业融资问题。基于“B-S模型”的可转债定价方法和基于实物期权的企业估值方法能够合理地为科技型中小企业的可转债融资定价。

混合所有制改革视阈下考虑努力互补的融资机制研究

基于混合所有制改革背景下国有企业引入民营资本可能出现事前和事后道德风险的情形,考虑努力互补因素构建了股权融资和含控制权安排的可转换债券融资契约模型,论证了各契约方存在努力互补时可转换债券融资相对于普通股权融资更有利于激励各契约方的努力水平,各契约方的期望收益更高,是一个严格的帕累托改进;采用可转换债券融资时,投资者行权前后存在不同的控制权安排比始终保持由同一契约方绝对控制更有利于解决双边道德风险问题。

基于布莱克-斯科尔斯模型的可转换债券的价值估计——以某上市公司可转债为例

可转换债券作为一种融合债券和股权双重特性,具备筹资和降低风险功能的多用途金融工具,它的价格确定一直受到广泛关注。文章通过分析可转换债券理论价值的构成得出可转换债券理论价值由一般债券部分价值和期权部分价值组成,并以银行股份有限公司于2021年发行的可转换债券为例,通过布莱克—斯科尔斯模型来估算可转换债券的理论价值,并将结果与其实际市价相较,分析价格偏差产生的原因,最后总结影响可转换债券理论价值的关键要素,以期为可转换债券的定价以及投资提供一些帮助。

旨在缓释发行银行风险激励效应的或有可转债设计与定价

为了缓释CoCos内蕴的对发行银行的风险激励效应,增强其市场吸引力,设计了一种关联发行银行财务困境成因的减记条款:对于发行银行因自身经营不善而导致的财务困境,此CoCos并不实施减记。在此基础上,运用马尔科夫状态转移方法和结构化定价方法,确定了CoCos价值、发行银行资产价值、股权价值和阈值的表达式。进一步,通过数值模拟与对比分析等发现:CoCos的适宜设计可藉其缓释发行银行的风险激励效应;所设计的减记条款具有情景依赖性:若发行银行经营能力下降,则其受经济周期所处状态的影响程度趋于增大;发行银行资产价值和CoCos价值均随风险的增大而减小,特别地,受风险偏好等因素的影响,在经济繁荣期上述相应效应呈现出非线性特征的“微笑”形态。

双分数随机波动率下可转换债券定价及实证分析

综合考虑资产价格收益率序列增量非平稳和非独立及波动率的随机性,建立双分数随机波动率下资产价格数学模型,研究可转换债券的定价。采用极大似然估计方法得到模型中参数,根据蒙特卡洛数值模拟方法,计算可转换债券价格。通过国投转债数据进行实证分析,并与其他模型对比。研究结果表明,双分数随机波动率下的可转换债券定价模型更符合实际金融市场。

分数布朗运动环境下具有机制转换的可转换债券定价模型

可转换债券是一种同时涉及债券、股票和期权的复合衍生证券,其定价问题一直是金融数学的热点问题之一。以多种股票数据为样本,考虑股票价格变动具有长程相依性和波动率非常数,在分数布朗运动环境下建立具有机制转换的股票价格模型,利用保险精算方法和蒙特卡洛模拟算法对可转换债券进行定价研究,并通过上银证券和上银转债市场数据进行实证分析。结果表明,分数布朗运动环境下具有机制转换的股票价格模型更适用于实际的金融市场。