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Stock options as barrier contingent claims


  • Jan Ericsson
  • Joel Reneby


A comprehensive model is suggested that values securities as options and consequently ordinary stock options as compound options. Extending the basic Black-Scholes model, it can incorporate common contractual features and stylized facts. More specifically, a closed form solution is derived for the price of a call option on a down-and-out call. It is then shown how the result obtained can be generalized in order to price options on complex corporate securities, allowing among other things for corporate taxation, costly financial distress and deviations from the absolute priority rule. The characteristics of the model are illustrated with numerical examples.

Suggested Citation

  • Jan Ericsson & Joel Reneby, 2003. "Stock options as barrier contingent claims," Applied Mathematical Finance, Taylor & Francis Journals, vol. 10(2), pages 121-147.
  • Handle: RePEc:taf:apmtfi:v:10:y:2003:i:2:p:121-147 DOI: 10.1080/1350486032000088921

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    References listed on IDEAS

    1. P. Carr, 1995. "Two extensions to barrier option valuation," Applied Mathematical Finance, Taylor & Francis Journals, vol. 2(3), pages 173-209.
    2. 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.
    3. Toft, Klaus Bjerre & Prucyk, Brian, 1997. " Options on Leveraged Equity: Theory and Empirical Tests," Journal of Finance, American Finance Association, vol. 52(3), pages 1151-1180, July.
    4. Jan Ericsson & Joel Reneby, 1998. "A framework for valuing corporate securities," Applied Mathematical Finance, Taylor & Francis Journals, vol. 5(3-4), pages 143-163.
    5. Geske, Robert, 1979. "The valuation of compound options," Journal of Financial Economics, Elsevier, vol. 7(1), pages 63-81, March.
    6. 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.
    7. Longstaff, Francis A & Schwartz, Eduardo S, 1995. " A Simple Approach to Valuing Risky Fixed and Floating Rate Debt," Journal of Finance, American Finance Association, vol. 50(3), pages 789-819, July.
    8. 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.
    9. Gregory R. Duffee, 1998. "The Relation Between Treasury Yields and Corporate Bond Yield Spreads," Journal of Finance, American Finance Association, vol. 53(6), pages 2225-2241, December.
    10. Rubinstein, Mark, 1994. " Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
    11. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
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    Cited by:

    1. Reindl, Johann & Stoughton, Neal & Zechner, Josef, 2013. "Market implied costs of bankruptcy," CFS Working Paper Series 2013/27, Center for Financial Studies (CFS).
    2. Hanke, Michael, 2005. "Pricing options on leveraged equity with default risk and exponentially increasing, finite maturity debt," Journal of Economic Dynamics and Control, Elsevier, vol. 29(3), pages 389-421, March.
    3. Marco Realdon, "undated". "Valuation of Put Options on Leveraged Equity," Discussion Papers 03/19, Department of Economics, University of York.
    4. Maria Carmen Badia Batlle & M. Mercedes Galisteo Rodriguez & M. Teresa Preixens Benedicto, 2006. "Un modelo de riesgo de credito basado en opciones compuestas con barrera. Aplicacion al mercado continuo espanol," Working Papers in Economics 156, Universitat de Barcelona. Espai de Recerca en Economia.

    More about this item


    model; stock options; corporate securities;

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing


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