Some characteristics of an equity security next-year impairment

  • Julien Azzaz
  • Stéphane Loisel
  • Pierre-E. ThérondEmail author
Original Research


In this paper, we propose some characteristics of next-year impairments in a generic Black and Scholes framework, with one equity security, and under International Financial Reporting Standards (IFRS) rules. We derive expression for the probability of impairment event for an equity-security recognized in the available-for-sale category. Our decomposition of this event is also useful to retrieve barrier options valuation methods. From there, we obtain an explicit formula for the first moment of impairment value and its cumulative distribution function, as well as sensitivities. Numerical studies are carried out on concrete securities. We also study a mean-preserving one-criterion proxy used by some insurance practitioners for the next-year impairment losses and discuss its relevance. More generally, our study paves the way for applications of financial mathematics techniques to accounting issues related to impairments in the IFRS framework.


Equity Impairment IFRS IAS 39 Available-for-sale (AFS) Rear-end up-and-out put option Barrier option 



This work has been mainly supported by the BNP Paribas Cardif Chair Management de la modélisation. The views expressed in this document are the authors owns and do not necessarily reflect those endorsed by BNP Paribas Cardif. The second author acknowledges support from the Milliman France Chair Actuariat Durable. The authors acknowledge financial support from the Europlace Institute of Finance (EIF) for research on impairment of financial assets (DéCAF project:


  1. Agostino M, Drago D, Silipo DB (2010) The value relevance of IFRS in the European banking industry. Rev Quant Financ Account 36(3):437–457CrossRefGoogle Scholar
  2. Batens N (2007) Modeling equity impairments. Belgian Actuarial Bull 7:24–33Google Scholar
  3. Bowen RM, Khan U, Rajgopal S (2009) The economic consequences of relaxing fair value accounting and impairment rules on banks during the financial crisis of 2008–2009, Working Paper, University of WashingtonGoogle Scholar
  4. Carr Peter (1995) Two extensions to barrier option valuation. Appl Math Financ 2(3):173–209CrossRefGoogle Scholar
  5. Carr P, Chou A (1997) Hedging complex barrier options, Working paperGoogle Scholar
  6. Chuang C-S (1996) Joint distribution of Brownian motion and its maximum, with a generalization to correlated BM and applications to barrier options. Stat Probab Lett 28:81–90CrossRefGoogle Scholar
  7. Couch R, Dothan M, Wu W (2012) Interest tax shields: a barrier options approach. Rev Quant Financ Account 39(1):123–146CrossRefGoogle Scholar
  8. Cox JC, Rubinstein M (1985) Options markets. Prentice-Hall, Upper Saddle RiverGoogle Scholar
  9. Grant T (2009) Technical accounting alert: impairment of available-for-sale equity investmentsGoogle Scholar
  10. Harrison JM (1985) Brownian motion and stochastic flow systems. Wiley, ColoradoGoogle Scholar
  11. Hui CH (1997) Time-Dependent Barrier Option Values. J Future Markets 17(6):667–688CrossRefGoogle Scholar
  12. Hull JC (2011) Options, futures and other derivatives. Prentice-Hall, Upper Saddle RiverGoogle Scholar
  13. Jaggi B, Winder JP, Lee C-F (2010) Is there a future for fair value accounting after the 2008–2009 financial crisis?. Rev Pac Basin Financ Markets Policies 13(3):469–493CrossRefGoogle Scholar
  14. Laux C, Leuz C (2009) The crisis of fair-value accounting: Making sense of the recent debate. Account Organiz Soc 34:826-834CrossRefGoogle Scholar
  15. Mozumder S, Sorwar G, Dowd K (2013) Option pricing under non-normality: a comparative analysis. Rev Quant Financ Account 40(2):273–292CrossRefGoogle Scholar
  16. Shreve SE (2004) Stochastic calculus for finance II: continuous-time models. Springer, BerlinGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Julien Azzaz
    • 1
  • Stéphane Loisel
    • 1
  • Pierre-E. Thérond
    • 1
    • 2
    Email author
  1. 1.Institut de Science Financière et d’AssurancesUniversité de LyonLyonFrance
  2. 2.Galea & AssociésParisFrance

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