scholarly journals Pricing Options and Convertible Bonds Based on an Actuarial Approach

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Jian Liu ◽  
Lizhao Yan ◽  
Chaoqun Ma
Keyword(s):  
Convertible Bonds ◽  
Convertible Bond ◽  
Chinese Stock Market ◽  
European Options ◽  
Bond Price ◽  
Pricing Options ◽  
Actuarial Approach ◽  
S Model ◽  
Actuarial Model ◽  
Parity Relation

This paper discusses the pricing problem of European options and convertible bonds using an actuarial approach. We get the pricing formula of European options, extend the pricing results to the case with continuous dividend, and then derive the call-put parity relation. Furthermore, we get the general expression of convertible bond price. Finally, we conduct a comparative analysis of numerical simulation and make an empirical analysis between the B-S model and the actuarial model using the actual data in the Chinese stock market. The empirical results show that the efficiency of the actuarial model is superior to the B-S model.

Pricing resettable convertible bonds using an integral equation approach

2019 ◽  
Vol 31 (4) ◽  
pp. 417-443
Author(s):  
Sha Lin ◽  
Song-Ping Zhu
Keyword(s):  
Integral Equation ◽  
Convertible Bonds ◽  
Convertible Bond ◽  
Equation Approach ◽  
Fair Price ◽  
Bond Price ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Integral Equation Approach ◽  
Increasing Function

Abstract In this paper, the fair price of an American-style resettable convertible bond (CB) under the Black–Scholes model with a particular reset clause is calculated. This is a challenging problem because an unknown optimal conversion price needs to be determined together with the bond price. There is also an additional complexity that the value of the conversion ratio will change when the underlying price touches the reset price. Because of the additional reset clause, the bond price is not always a monotonically increasing function with the underlying price, which is impossible for other types of the CBs. Of course, the problem can be dealt with using the Monte-Carlo simulation. But, a partial differential equation (PDE)/integral equation approach is far superior in terms of computational efficiency. Fortunately, after establishing the PDE system governing the bond price, we are able to present an integral equation representation by applying the incomplete Fourier transform on the PDE system.

scholarly journals Dividends Sharing Convertible Bonds Pricing and Numerical Evaluation

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Xu Guo ◽  
Haiyang Wang
Keyword(s):  
New York ◽  
Convertible Bonds ◽  
Obstacle Problems ◽  
Convertible Bond ◽  
Bond Price ◽  
Parabolic Pdes ◽  
Nonlinear Parabolic Pdes ◽  
Nonlinear Parabolic ◽  
Underlying Stocks ◽  
Discrete Dividends

The convertible bond is becoming one of the most important financial instruments for the company to raise capital fund since it was first issued by American New York Erie Company in 1843. In this paper, it is the first time to study the pricing problem for convertible bond whose underlying stocks pay dividends via the reflected backward stochastic differential equations. Associating the solutions of reflected BSDEs with the obstacle problems for nonlinear parabolic PDEs, we establish the pricing formulas for convertible bonds with continuous and discrete dividends by means of the viscosity solutions for some PDEs. Besides, we also derive the price of convertible bonds with higher borrowing rate which is realistic in the financial market. Then the numerical evaluations are provided by the radial basis functions method. Moreover, we discuss the influence of dividends paying as well as higher borrowing rate on the convertible bond price at last.

Pricing Convertible Bond in Uncertain Financial Market

2021 ◽  
pp. 2150007
Author(s):  
Zhiqiang Zhang ◽  
Zhenfang Wang ◽  
Xiaowei Chen
Keyword(s):  
Differential Equation ◽  
Financial Market ◽  
Stock Price ◽  
Uncertainty Theory ◽  
Convertible Bonds ◽  
Convertible Bond ◽  
Uncertain Differential Equation ◽  
Numerical Examples ◽  
Liu Process ◽  
Uncertain Calculus

This paper is devoted to evaluating the convertible bonds within the framework of uncertainty theory. Under the assumption that the underlying stock price follows an uncertain differential equation driven by Liu process, the price formulas of convertible bonds and the callable convertible bonds are derived by using the method of uncertain calculus. Finally, two numerical examples are discussed.

ON THE VALUATION OF DERIVATIVES WITH SNAPSHOT RESET FEATURES

2008 ◽  
Vol 11 (08) ◽  
pp. 905-941 ◽  
Author(s):  
ERIC C. K. YU ◽  
WILLIAM T. SHAW
Keyword(s):  
Convertible Bonds ◽  
Convertible Bond ◽  
Put Options ◽  
Risk Characteristics ◽  
Black Scholes ◽  
Barrier Type ◽  
Simple Change ◽  
Discontinuous Nature ◽  
Change Of Variable ◽  
Digital Options

We propose a general approach that requires only a simple change of variable that keeps the valuation of call and put options (convertible bonds) with strike (conversion) price resets two-dimensional in the classical Black–Scholes setting. A link between reset derivatives, compound options and "discrete barrier" type options, when there is one reset is then discussed, from which we analyze the risk characteristics of reset derivatives, which can be significantly different from their vanilla counterparts. We also generalize the prototype reset structure and show that the delta and gamma of a convertible bond with reset can both be negative. Finally, we show that the "waviness" property found in the delta and gamma of some reset derivatives is due to the discontinuous nature of the reset structure, which is closely linked to digital options.

scholarly journals The Analysis of Chinese Convertible Bond Market

2020 ◽  
Vol 6 (2) ◽  
pp. p104
Author(s):  
Yuxin Tian ◽  
Jun Chen
Keyword(s):  
Portfolio Management ◽  
Convertible Bonds ◽  
Bond Market ◽  
Comprehensive Analysis ◽  
Convertible Bond ◽  
Historical Evolution ◽  
Chinese Market ◽  
Valuation Model ◽  
Black Scholes Model ◽  
Black Scholes

Convertible bond is a type of hybrid security with both bond- and stock-like features. The Chinese market of convertible bonds has developed dramatically during the last decade. This paper will conduct a comprehensive analysis of this market. Firstly, a brief introduction of convertible bond and the historical evolution of this market in China is presented, then we analyze various investment risks related to convertible bonds. Next, this paper proposes the basic valuation model for convertible bonds, which is the Black-Scholes model and modifies it by taking the delusion effect of conversion into account, leading to the Gailai-Schneller model. In addition, the differences of the outcomes obtained by these two models are compared and analyzed based on the pricing of Shanghai Electric convertible bond. In the sixth part, this paper mainly explains two types of applications of convertible bonds in portfolio management. In the end, several problems existing in Chinese convertible market as well as some suggestions for solving them are discussed.

Skewness of Kurtosis?: Using Corrado and Su (1996)‘s Model

2008 ◽  
Vol 16 (1) ◽  
pp. 1-20
Author(s):  
Sol Kim
Keyword(s):  
Options Market ◽  
Index Options ◽  
Pricing Options ◽  
Risk Neutral ◽  
Out Of Sample ◽  
S Model ◽  
Skewness And Kurtosis

For the KOSPI 200 index options market. we examine the power of influence on pricing options of the skewness and the kurtosis of the risk neutral distribution. We compare the Black and Scholes (1973) model which does not consider the skewness or the kurtosis of the risk neutral distribution with Corrado and sue 1996)’s model which consider both the skewness and the kurtosis and the models which consider only the skewness or the kurtosis. It is found that Corrado and sue 1996)‘s model which consider both skewness and kurtosis shows the best performance closely followed by the model which consider only the skewness for tile in-sample pricing and the out-of-sample pricing. As a result. it contributes to pricing options to consider both skewness and kurtosis and the skewness is more important factor for pricing options than the kurtosis.

scholarly journals Pricing Convertible Bonds with Credit Risk under Regime Switching and Numerical Solutions

2014 ◽  
Vol 2014 ◽  
pp. 1-13
Author(s):  
Wei-Guo Zhang ◽  
Ping-Kang Liao
Keyword(s):  
Credit Risk ◽  
Regime Switching ◽  
Numerical Solutions ◽  
Dilution Effect ◽  
Convertible Bonds ◽  
Bond Pricing ◽  
Convertible Bond ◽  
Pricing Model ◽  
Black Scholes ◽  
The Impact

This paper discusses the convertible bonds pricing problem with regime switching and credit risk in the convertible bond market. We derive a Black-Scholes-type partial differential equation of convertible bonds and propose a convertible bond pricing model with boundary conditions. We explore the impact of dilution effect and debt leverage on the value of the convertible bond and also give an adjustment method. Furthermore, we present two numerical solutions for the convertible bond pricing model and prove their consistency. Finally, the pricing results by comparing the finite difference method with the trinomial tree show that the strength of the effect of regime switching on the convertible bond depends on the generator matrix or the regime switching strength.

scholarly journals A Simple and Precise Method for Pricing Convertible Bond with Credit Risk

2019 ◽  
Author(s):  
Tim Xiao
Keyword(s):  
Probability Distribution ◽  
Credit Risk ◽  
Stock Price ◽  
Convertible Bonds ◽  
Convertible Bond ◽  
Financial Instruments ◽  
Market Prices ◽  
Precise Method ◽  
Large Movement ◽  
Arbitrage Strategy

This paper presents a new model for valuing hybrid defaultable financial instruments, such as, convertible bonds. In contrast to previous studies, the model relies on the probability distribution of a default jump rather than the default jump itself, as the default jump is usually inaccessible. As such, the model can back out the market prices of convertible bonds. A prevailing belief in the market is that convertible arbitrage is mainly due to convertible underpricing. Empirically, however, we do not find evidence supporting the underpricing hypothesis. Instead, we find that convertibles have relatively large positive gammas. As a typical convertible arbitrage strategy employs delta-neutral hedging, a large positive gamma can make the portfolio highly profitable, especially for a large movement in the underlying stock price.

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

2021 ◽  
Vol 3 (6) ◽  
Author(s):  
Zhang Heng ◽  
Yuyang Zhao ◽  
Qiguang An
Keyword(s):  
Credit Rating ◽  
Market Price ◽  
Convertible Bonds ◽  
Bond Market ◽  
Convertible Bond ◽  
Average Deviation ◽  
Healthy Development ◽  
Credit Risks ◽  
Deviation Rate ◽  
The Impact

At present, further research and exploration on credit risks are being carried out in the global field, and increasingly profound modern 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 Fernandes(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 than 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.

scholarly journals Mandatory Convertible Bonds and the Agency Problem

2019 ◽  
Vol 11 (15) ◽  
pp. 4074
Author(s):  
Angel Huerga ◽  
Carlos Rodríguez-Monroy
Keyword(s):  
Default Risk ◽  
Agency Problem ◽  
Balance Sheet ◽  
Convertible Bonds ◽  
Convertible Bond ◽  
Financial Sustainability ◽  
Stable Growth ◽  
Debt Holders ◽  
The Empirical Analysis

A large proportion of the academic literature about the agency problem focuses on corporate governance or the instruments that can be used to balance the incentives of shareholders and debt holders. Following the real options company valuation framework, one method to increase shareholder value involves increasing the intrinsic risk of the firm; however, such a practice reduces the bondholder value. We analyzed an innovative balance sheet instrument, the mandatory convertible bond, as a means to increase financial sustainability of companies, improving the value for shareholders without increasing the perceived default risk. The results of the empirical analysis illustrate that for companies in a weak credit position, the agency problem can be mitigated by the issuance of mandatory convertible bonds, which allows managers to increase company risk without being detrimental for bondholders. However, when the probability of distress is small, shareholders have less incentive to increase company risk than in a company funded by mandatory convertible bonds, being more aligned with bondholders. A better alignment of debt holders and shareholders incentives reduces inefficiencies, mitigates the probably of distress, and improves the long-term financial sustainability of companies and can promote stable growth and innovation.

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