On pricing of corporate securities in the case of jump-diffusion

Structural models of credit risk are known to present vanishing spreads at very short maturities. This shortcoming, which is due to the diffusive behavior assumed for asset values, can be circumvented by considering discontinuities of the jump type in their evolution over time. In this paper, we extend the pricing model for corporate bond and determine the default probability in jump-diffusion model to address this issue. To make the problem clearly, we first investigate the case that the firm value follows a geometric Brownian motion under similar assumptions to those in Black and Scholes（1973）, Briys and de Varenne（1997）, i.e, the default barrier is KD （t, T） and the recovery rate is （1 -w）, where D （t, T） is the price of zero coupon default free bond and w is a constant （0 〈 w 〈 1）. By changing the numeraire, we obtain the closed-form solution for both the price of bond and default probability. Further, we consider the case of jump-diffusion and suppose that a firm will go bankruptcy if its value Vt 〈 KD （t, T） and at the same time, the bondholder will receive （1 - w） vt/k By introducing the Green function of PDE with absorbing boundary and converting the problem to an II-type Volterra integral equation, we get the closed-form expressions in series form for bond price and corresponding default probability. Numerical results are presented to show the impact of different parameters to credit spread of bond.

A Bond Pricing Model with Credit Migration Risk:Different Upgrade and Downgrade Thresholds

In this paper, a new corporate bond pricing model with credit migration risk is proposed. This model sets different thresholds for the rising or falling of credit ratings, which forms a buffer zone that could reduce the frequency of credit rating changes. Mathematically, this model is a system of partial differential equations with overlapping area. The existence, uniqueness, regularity and asymptotic behavior of the solution are obtained. Furthermore, a numerical scheme and its stability, convergence and accuracy are discussed in detail. Calibration and analysis of the parameters are also suggested.

High-Speed Rail Service and the Issuance of Municipal Corporate Bonds

This study uses the difference-in differences method to test the impact of a high-speed rail(HSR)service on the issuance of municipal corporate bonds(MCB)based on panel data for prefecture-level cities in China from 2003 to 2016.The study has three findings.First,HSR increased the scale of the issuance of MCB significantly.After conducting a series of robustness tests,the above conclusion remained robust.Second,HSR affected the issuance of MCB by increasing the city's financing demands and improving the city's financing capacity.Third,the effect of HSR on the issuance of MCB varied from city to city.Specifically,the promotion of the opening of HSR to the issuance of MCB was concentrated in remote and fast growing cities.High-speed rail can also effectively reduce the cost and shrink credit spreads of the MCB.This paper shows that it is necessary to further optimize the layout of HSR,release and exploit the financial resource reallocation effect of HSR,and provide financial support to the high-quality development of cities.

An Overview of China’s Bond Markets

This paper introduces the current structure and practice of China＇s bond markets in general and corporate bond market in particular. It analyses the factors behind the slow development of China＇s bond markets： heavy government intervention, underdevelopment of direct financing, etc. It also puts forward policy options in promoting bonds markets development, including reform of government regulatory framework and improving financial intermediaries and services.