scholarly journals Is the Jump-Diffusion Model a Good Solution for Credit Risk Modeling? The Case of Convertible Bonds

2019 ◽  
Author(s):  
Tim Xiao
Keyword(s):  
Credit Risk ◽  
Diffusion Model ◽  
Stock Price ◽  
Jump Diffusion ◽  
Convertible Bonds ◽  
Reduced Form ◽  
Risk Modeling ◽  
Jump Diffusion Model ◽  
Credit Risk Modeling ◽  
Arbitrage Strategy

This paper argues that the reduced-form jump diffusion model may not be appropriate for credit risk modeling. To correctly value hybrid defaultable financial instruments, e.g., convertible bonds, we present a new framework that 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 Is the Jump-Diffusion Model a Good Solution for Credit Risk Modeling? The Case of Convertible Bonds

2019 ◽  
Author(s):  
Tim Xiao
Keyword(s):  
Credit Risk ◽  
Diffusion Model ◽  
Stock Price ◽  
Jump Diffusion ◽  
Convertible Bonds ◽  
Reduced Form ◽  
Risk Modeling ◽  
Jump Diffusion Model ◽  
Credit Risk Modeling ◽  
Arbitrage Strategy

This paper argues that the reduced-form jump diffusion model may not be appropriate for credit risk modeling. To correctly value hybrid defaultable financial instruments, e.g., convertible bonds, we present a new framework that 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 Is the Jump-Diffusion Model a Good Solution for Credit Risk Modeling? The Case of Convertible Bonds

2019 ◽  
Author(s):  
Tim Xiao
Keyword(s):  
Credit Risk ◽  
Diffusion Model ◽  
Stock Price ◽  
Jump Diffusion ◽  
Convertible Bonds ◽  
Reduced Form ◽  
Risk Modeling ◽  
Jump Diffusion Model ◽  
Credit Risk Modeling ◽  
Arbitrage Strategy

This paper argues that the reduced-form jump diffusion model may not be appropriate for credit risk modeling. To correctly value hybrid defaultable financial instruments, e.g., convertible bonds, we present a new framework that 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 Is the Jump-Diffusion Model a Good Solution for Credit Risk Modeling? The Case of Convertible Bonds

2019 ◽  
Author(s):  
Tim Xiao
Keyword(s):  
Credit Risk ◽  
Diffusion Model ◽  
Stock Price ◽  
Jump Diffusion ◽  
Convertible Bonds ◽  
Reduced Form ◽  
Risk Modeling ◽  
Jump Diffusion Model ◽  
Credit Risk Modeling ◽  
Arbitrage Strategy

This paper argues that the reduced-form jump diffusion model may not be appropriate for credit risk modeling. To correctly value hybrid defaultable financial instruments, e.g., convertible bonds, we present a new framework that 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 LONG MEMORY VERSION OF STOCHASTIC VOLATILITY JUMP-DIFFUSION MODEL WITH STOCHASTIC INTENSITY

2020 ◽  
Vol 38 (2) ◽  
Author(s):  
Somayeh Fallah ◽  
Farshid Mehrdoust
Keyword(s):  
Stochastic Volatility ◽  
Long Range ◽  
Diffusion Model ◽  
Long Memory ◽  
Stock Price ◽  
Real Data ◽  
Jump Diffusion ◽  
Heston Model ◽  
Long Range Dependence ◽  
Jump Diffusion Model

It is widely accepted that certain financial data exhibit long range dependence. We consider a fractional stochastic volatility jump diffusion model in which the stock price follows a double exponential jump diffusion process with volatility described by a long memory stochastic process and intensity rate expressed by an ordinary Cox, Ingersoll, and Ross (CIR) process. By calibrating the model with real data, we examine the performance of the model and also, we illustrate the role of long range dependence property by comparing our presented model with the Heston model.

scholarly journals Valuation of Game Options in Jump-Diffusion Model and with Applications to Convertible Bonds

2009 ◽  
Vol 2009 ◽  
pp. 1-17 ◽  
Author(s):  
Lei Wang ◽  
Zhiming Jin
Keyword(s):  
Free Boundary ◽  
Diffusion Process ◽  
Stock Price ◽  
Free Boundary Problems ◽  
Jump Diffusion ◽  
Convertible Bonds ◽  
Simple Application ◽  
Boundary Problems ◽  
Game Options ◽  
Jump Diffusion Model

Game option is an American-type option with added feature that the writer can exercise the option at any time before maturity. In this paper, we consider some type of game options and obtain explicit expressions through solving Stefan(free boundary) problems under condition that the stock price is driven by some jump-diffusion process. Finally, we give a simple application about convertible bonds.

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