A comprehensive unified model of structural and reduced form type for defaultable fixed income bonds

Document Type : Research Paper

Authors

Faculty of Mathematics‎, ‎Kim Il Sung University‎, ‎Taesong District‎, ‎Pyongyang‎, ‎D‎. ‎P‎. ‎R‎. ‎Korea.

Abstract

‎The aim of this paper is to generalize the comprehensive structural model for defaultable fixed income bonds (considered in R‎. ‎Agliardi‎, ‎A comprehensive structural model for defaultable fixed-income bondsو Quant‎. ‎Finance 11 (2011)‎, ‎no‎. ‎5‎, ‎749--762.) into a comprehensive unified model of structural and reduced form models‎. ‎In our model the bond holders receive the deterministic coupon at predetermined coupon dates and the face value (debt) and the coupon at the maturity as well as the effect of government taxes which are paid on the proceeds of an investment in bonds is considered‎. ‎The expected default event occurs when the equity value is not enough to pay coupon or debt at the coupon dates or maturity and an unexpected default event can occur at any time interval with the probability of given default intensity‎. ‎We consider the model and pricing formula for equity value and using it calculate expected default barrier‎. ‎Then we provide pricing model and formula for defaultable corporate bonds with discrete coupons‎, ‎and consider the duration and the effect of the government taxes‎.

Keywords

Main Subjects

References

R. Agliardi, A comprehensive structural model for defaultable fixed-income bonds, Quant. Finance 11 (2011), no. 5, 749--762.
L.V. Ballestra and G. Pacelli, Valuing risky debt: A new model combining structural information with the reduced-form approach, Insurance Math. Econom. 55 (2014) 261--271.
L.V. Ballestra and G. Pacelli, A numerical method to price defaultable bonds based on the Madan and Unal credit risk model, Appl. Math. Finance 16 (2009), no. 1-2, 17--36.
T.R. Bielecki and M. Rutkowski, Credit Risk, Modeling, Valuation and Hedging, Springer-Verlag, Berlin, Heidelberg, 2002.
P. Buchen, The pricing of dual-expiry exotics, Quant. Finance 4 (2004), no. 1, 101--108.
L. Cathcart and L. El-Jahel, Semi-analytical pricing of defaultable bonds in a signalling jump-default model, J. Comput. Finance 6 (2003) 91-108.
L. Cathcart and L. El-Jahel, Pricing defaultable bonds: a middle-way approach between structural and reduced-form models, Quant. Finance 6 (2006), no. 3, 243--253.
D. Duffie, J. Kenneth and J. Singleton, Modeling term structures of defaultable bonds, Rev. Financ. Stud. 12 (1999), no. 4, 687--720.
R. Geske, The valuation of corporate liabilities as compound options, J. Finan. Quant. Anal. 12 (1977), no. 4, 541--552.
R.A. Jarrow, Risky coupon bonds as a portfolio of zero-coupon bonds, Finan. Res. Lett. 1 (2004), no. 2, 100--105.
L.S. Jiang, Mathematical Models and Methods of Option Pricing, World Scientific, 2005.
D.B. Madan and H. Unal, Pricing the risk of default, Rev. Derivatives Res. 2 (1998) 121--160.
 D.B. Madan and H. Unal, A two-factor hazard-rate model for pricing risky debt and the term structure of credit spreads, J. Financ. Quant. Anal. 35 (2000) 43--65.
R.C. Merton, On the pricing of corporate debt: the risk structure of interest rates, J. Finance 29 (1974), no. 2, 449--470.
H.C. O and M.C. Kim, Higher order binary options and multiple expiry exotics, Electron. J. Math. Anal. Appl. 1 (2013), no. 2, 247--259
H.C. O and J.S. Kim, General properties of solutions to inhomogeneous Black-Scholes equations with discontinuous maturity payoffs, J. Differential Equations 260 (2016), no. 4, 3151--3172.
H.C. O, D.H. Kim and C.H. Pak, Analytical pricing of defaultable discrete coupon bonds in unified two-factor model of structural and reduced form models, J. Math. Anal. Appl. 416 (2014), no. 1, 314--334.
H.C. O, D.H. Kim, J.J. Jo and S.H. Ri, Integrals of higher binary options and defaultable bonds with discrete default information, Electron. J. Math. Anal. Appl. 2 (2014), no. 1, 190--214.
H.C. O and N. Wan, Analytical pricing of defaultable bond with stochastic default intensity, Arxiv:1303.1298 [q-_n.PR], DOI:10.2139/ssrn.723601.
P. Wilmott, Derivatives: the Theory and Practice of Financial Engineering, John Wiley & Sons, 1998
P. Wilmott, S. Howison and J. Dewynne, The Mathematics of Financial Derivatives, A Student Introduction, Cambridge Univ. Press, Cambridge, 1995.
Bulletin of the Iranian Mathematical Society
Volume 43, Issue 3
June 2017
Pages 575-599

Files

History

  • Receive Date: 25 August 2014
  • Revise Date: 01 December 2015
  • Accept Date: 09 December 2015

Share

How to cite

Statistics