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Pricing Corporate Securities Under Noisy Asset Information

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  • Rüdiger Frey
  • Thorsten Schmidt

Abstract

This paper considers the pricing of corporate securities of a given firm, in particular equity, when investors do not have full information on the firm's asset value. We show that under noisy asset information, the pricing of corporate securities leads to a nonlinear filtering problem. This problem is solved by a Markov chain approximation, leading to an efficient finite‐dimensional approximative filter for the asset value. We discuss several applications and illustrate our results with a simulation study.

Suggested Citation

  • Rüdiger Frey & Thorsten Schmidt, 2009. "Pricing Corporate Securities Under Noisy Asset Information," Mathematical Finance, Wiley Blackwell, vol. 19(3), pages 403-421, July.
    • Handle: RePEc:bla:mathfi:v:19:y:2009:i:3:p:403-421
    DOI: 10.1111/j.1467-9965.2009.00374.x
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    References listed on IDEAS

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    1. Delia Coculescu & Hélyette Geman & Monique Jeanblanc, 2008. "Valuation of default-sensitive claims under imperfect information," Finance and Stochastics, Springer, vol. 12(2), pages 195-218, April.
    2. Vadim Linetsky, 2006. "Pricing Equity Derivatives Subject To Bankruptcy," Mathematical Finance, Wiley Blackwell, vol. 16(2), pages 255-282, April.
    3. Leland, Hayne E & Toft, Klaus Bjerre, 1996. "Optimal Capital Structure, Endogenous Bankruptcy, and the Term Structure of Credit Spreads," Journal of Finance, American Finance Association, vol. 51(3), pages 987-1019, July.
    4. Black, Fischer & Cox, John C, 1976. "Valuing Corporate Securities: Some Effects of Bond Indenture Provisions," Journal of Finance, American Finance Association, vol. 31(2), pages 351-367, May.
    5. Merton, Robert C, 1974. "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 29(2), pages 449-470, May.
    6. Duffie, Darrell & Lando, David, 2001. "Term Structures of Credit Spreads with Incomplete Accounting Information," Econometrica, Econometric Society, vol. 69(3), pages 633-664, May.
    7. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
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    Citations

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    Cited by:

    1. Çetin, Umut, 2012. "On absolutely continuous compensators and nonlinear filtering equations in default risk models," Stochastic Processes and their Applications, Elsevier, vol. 122(11), pages 3619-3647.
    2. Rüdiger Frey & Wolfgang Runggaldier, 2010. "Pricing credit derivatives under incomplete information: a nonlinear-filtering approach," Finance and Stochastics, Springer, vol. 14(4), pages 495-526, December.
    3. Rubesam, Alexandre & Zimmermann, Paul, 2025. "Sideshow or center stage? Information transmission between CDS and equity markets," Journal of Financial Intermediation, Elsevier, vol. 63(C).
    4. Delia Coculescu & Gabriele Visentin, 2017. "A default system with overspilling contagion," Papers 1709.09255, arXiv.org, revised May 2023.
    5. Tolulope Fadina & Thorsten Schmidt, 2024. "The Unfairness of $\varepsilon$-Fairness," Papers 2405.09360, arXiv.org, revised Jun 2024.
    6. Ruediger Frey & Lars Roesler & Dan Lu, 2017. "Corporate Security Prices in Structural Credit Risk Models with Incomplete Information: Extended Version," Papers 1701.04780, arXiv.org, revised May 2017.
    7. Tolulope Fadina & Thorsten Schmidt, 2019. "Default Ambiguity," Risks, MDPI, vol. 7(2), pages 1-17, June.
    8. Delia Coculescu & Monique Jeanblanc & Ashkan Nikeghbali, 2012. "Default times, no-arbitrage conditions and changes of probability measures," Finance and Stochastics, Springer, vol. 16(3), pages 513-535, July.
    9. Zorana Grbac & Simone Pavarana & Thorsten Schmidt & Peter Tankov, 2025. "Propagation of carbon price shocks through the value chain: the mean-field game of defaults," Papers 2507.11353, arXiv.org.
    10. Lin, Yan-Ting & Nienhaus, Martin, 2015. "The non-diversifiable risk of financial reporting system: Evidence from the German market," Advances in accounting, Elsevier, vol. 31(2), pages 197-208.
    11. Umut c{C}etin, 2012. "On absolutely continuous compensators and nonlinear filtering equations in default risk models," Papers 1205.1154, arXiv.org.
    12. Fadina, Tolulope & Schmidt, Thorsten, 2025. "Default Ambiguity," Center for Mathematical Economics Working Papers 710, Center for Mathematical Economics, Bielefeld University.
    13. Fontana, Claudio & Schmidt, Thorsten, 2018. "General dynamic term structures under default risk," Stochastic Processes and their Applications, Elsevier, vol. 128(10), pages 3353-3386.
    14. Sandrine Gumbel & Thorsten Schmidt, 2021. "Defaultable term structures driven by semimartingales," Papers 2103.01577, arXiv.org, revised Aug 2021.
    15. Rüdiger Frey & Thorsten Schmidt, 2012. "Pricing and hedging of credit derivatives via the innovations approach to nonlinear filtering," Finance and Stochastics, Springer, vol. 16(1), pages 105-133, January.
    16. Frank Gehmlich & Thorsten Schmidt, 2014. "Dynamic Defaultable Term Structure Modelling beyond the Intensity Paradigm," Papers 1411.4851, arXiv.org, revised Jul 2015.

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