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A latent process model for the pricing of corporate securities

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Abstract

We propose a structural model with a joint process of tangible assets (marker) and firm status for the pricing of corporate securities. The firm status is assumed to be latent or unobservable, and default occurs when the firm status process reaches a default threshold at the first time. The marker process is observable and assumed to be correlated with the latent firm status. The recovery upon default is a fraction of tangible assets at the time of default. Our model can evaluate both the corporate debt and equity to fit their market prices in a unified framework. When the two processes are perfectly correlated, our model is reduced to the seminal Black–Cox model. Numerical examples are given to support the usefulness of our model.

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References

  • Altman EI (1968) Financial ratios, discriminant analysis and the prediction of corporate bankruptcy. J Financ 23: 589–609

    Article  Google Scholar 

  • Black F, Cox J (1976) Valuing corporate securities: some effects on bond indenture provisions. J Financ 31: 351–367

    Article  Google Scholar 

  • Briys E, de Varenne F (1997) Valuing risky fixed debt: an extension. J Financ Quant Anal 32: 239–248

    Article  Google Scholar 

  • Chen N, Kou S (2005) Credit spreads, optimal capital structure, and implied volatility with endogenous default and jump risk. Working paper, Columbia University

  • CreditMetricsTM (1997) JP Morgan

  • Fons JS (1994) Using default rates to model the term structure of credit risk. Financ Anal J September-October:25–32

  • Giesecke K (2004) Correlated default with incomplete information. J Bank Financ 28: 1521–1545

    Article  Google Scholar 

  • Jarrow RA, Turnbull SM (1995) Pricing derivatives on financial securities subject to credit risk. J Financ 50: 53–86

    Article  Google Scholar 

  • Karatzas I, Shreve SE (1988) Brownian motion and stochastic calculus. Springer, Heidelberg

    MATH  Google Scholar 

  • Kijima M (1998) Monotonicities in a Markov chain model for valuing corporate bonds subject to credit risk. Math Financ 8: 229–247

    Article  MATH  Google Scholar 

  • Kijima M, Suzuki T (2001) A jump-diffusion model for pricing corporate debt securities in a complex capital structure. Quant Financ 1: 611–620

    Article  Google Scholar 

  • Lee T, DeGruttola V, Schoenfeld D (2000) A model for markers and latent health status. J R Stat Soc 62: 747–762

    Article  MATH  MathSciNet  Google Scholar 

  • Leland H (1994) Corporate debt value, bond covenants, and optimal capital structure. J Financ 49: 1213–1252

    Article  Google Scholar 

  • Longstaff F, Schwartz E (1995) A simple approach to valuing risky fixed and floating rate debt. J Financ 50: 789–819

    Article  Google Scholar 

  • Madan D, Unal H (2000) A two-factor hazard rate model for pricing risky debt and the term structure of credit spreads. J Financ Quant Anal 35: 43–65

    Article  Google Scholar 

  • Mella-Barral P, Perraudin W (1997) Strategic debt service. J Financ 52: 531–556

    Article  Google Scholar 

  • Merton RC (1974) On the pricing of corporate debt: The risk structure of interest rates. J Financ 29: 449–470

    Article  Google Scholar 

  • Merton RC (1976) Option pricing when underlying stock returns are discontinuous. J Financ Econ 3: 125–144

    Article  MATH  Google Scholar 

  • Whitmore GA, Crowder MJ, Lawless JF (1998) Failure inference from a marker process based on a bivariate Wiener model. Lifetime Data Anal 4: 229–251

    Article  MATH  Google Scholar 

  • Zhou C (2001) The term structure of credit spreads with jump risk. J Bank Financ 25: 2015–2040

    Article  Google Scholar 

Download references

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Correspondence to Masaaki Kijima.

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Kijima, M., Suzuki, T. & Tanaka, K. A latent process model for the pricing of corporate securities. Math Meth Oper Res 69, 439–455 (2009). https://doi.org/10.1007/s00186-008-0246-5

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  • DOI: https://doi.org/10.1007/s00186-008-0246-5

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