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.

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.

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.

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.

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.

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.

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.