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.

scholarly journals European Spread Option Pricing with the Floating Interest Rate for Uncertain Financial Market

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Lidong Zhang ◽  
Yanmei Sun ◽  
Xiangbo Meng
Keyword(s):  
Differential Equation ◽  
Interest Rate ◽  
Financial Market ◽  
Stock Price ◽  
Numerical Algorithms ◽  
Uncertain Differential Equation ◽  
Spread Options ◽  
Put Option ◽  
Pricing Problems ◽  
Spread Option

In this paper, we investigate the pricing problems of European spread options with the floating interest rate. In this model, uncertain differential equation and stochastic differential equation are used to describe the fluctuation of stock price and the floating interest rate, respectively. We derive the pricing formulas for spread options including the European spread call option and the European spread put option. Finally, numerical algorithms are provided to illustrate our results.

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.

Contingent conversion convertible bond: New avenue to raise bank capital

2017 ◽  
Vol 04 (01) ◽  
pp. 1750001 ◽  
Author(s):  
Francesca Erica Di Girolamo ◽  
Francesca Campolongo ◽  
Jan De Spiegeleer ◽  
Wim Schoutens
Keyword(s):  
Interest Rate ◽  
Financial Market ◽  
Convertible Bonds ◽  
Share Price ◽  
Convertible Bond ◽  
Bank Capital ◽  
Rate Process ◽  
Depth Analysis ◽  
Stochastic Interest ◽  
Market Product

This paper provides an in-depth analysis of the structuring and the pricing of an innovative financial market product. This instrument is called a contingent conversion convertible bond or “CoCoCo”. This hybrid bond is itself a combination of two other hybrid instruments: a contingent convertible (“CoCo”) and a convertible bond. This combination introduces more complexity in the structure but it also allows investors to profit from strong share price performances. This upside potential is added on top of the normal contingent convertible mechanics of CoCos, which expose the investors to mainly downside risk. First, we explain how the features of the contingent convertible bonds on one side and the features of the standard convertible bonds on the other side are combined. Thereafter, we propose a pricing approach which moves away from the standard Black[Formula: see text]Scholes setting. The CoCoCos are evaluated using the Heston process to which a Hull-White interest rate process has been added. We demonstrate the importance of using a stochastic interest rate when modeling this instrument. Finally we quantify the loss absorbing capacity of this instrument.

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 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 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 Structural Credit Risk Model with Jumps Based on Uncertainty Theory

2021 ◽  
Author(s):  
Hong Huang ◽  
Yufu Ning
Keyword(s):  
Differential Equation ◽  
Credit Risk ◽  
Behavioral Finance ◽  
Uncertainty Theory ◽  
Risk Model ◽  
Credit Default Swap ◽  
Uncertain Differential Equation ◽  
Underlying Asset ◽  
Stock Value ◽  
Proposed Model

Abstract Traditional finance studies of credit risk structured models are based on the assumption that the price of the underlying asset obeys a stochastic differential equation. However, according to behavioral finance, the price of the underlying asset is not entirely stochastic, and the credibility of financial investors also plays a very important role in asset prices. In this paper we introduce uncertainty theory to describe these credibility of investors and propose a new credit risk structured model with jumps based on the assumption that the underlying asset is described by an uncertain differential equation with jumps. The company default belief degree formula, zero coupon bond value and stock value formula are formulated. Company bond credit spread and credit default swap (CDS) pricing are studied as applications of the proposed model in uncertain markets.

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 Risk-Neutral Pricing Method of Options Based on Uncertainty Theory

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2285
Author(s):  
Hong Huang ◽  
Yufu Ning
Keyword(s):  
Stock Price ◽  
Uncertainty Theory ◽  
Independent Increment ◽  
Special Kind ◽  
Uncertain Process ◽  
Put Options ◽  
Liu Process ◽  
Stationary Independent Increment ◽  
Risk Neutral ◽  
Relationship Of

In order to rationally deal with the belief degree, Liu proposed uncertainty theory and refined into a branch of mathematics based on normality, self-duality, sub-additivity and product axioms. Subsequently, Liu defined the uncertainty process to describe the evolution of uncertainty phenomena over time. This paper proposes a risk-neutral option pricing method under the assumption that the stock price is driven by Liu process, which is a special kind of uncertain process with a stationary independent increment. Based on uncertainty theory, the stock price’s distribution and inverse distribution function under the risk-neutral measure are first derived. Then these two proposed functions are applied to price the European and American options, and verify the parity relationship of European call and put options.

scholarly journals Factors Affecting The Equity Price Impacts Of Convertible Bonds

2011 ◽  
Vol 8 (4) ◽  
pp. 79 ◽  
Author(s):  
Bruce R. Kohlman ◽  
Robert C. Radcliffe
Keyword(s):  
Stock Returns ◽  
Stock Price ◽  
Convertible Bonds ◽  
Equity Returns ◽  
Convertible Bond ◽  
Factors Affecting ◽  
Price Impacts ◽  
Bond Issues ◽  
Abnormal Stock Returns ◽  
Equity Price

This study examines abnormal stock returns associated with both the date a convertible bond issue is announced and the date it is sold. Results suggest the negative stock price effects observed I this and previous studies are due to the equity component inherent in convertible bonds, and an easily observed measure of that equity component is offered. In addition, results suggest that convertible bond issues sold by firms with previously issued outstanding convertibles are met with larger negative abnormal equity returns.

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