Skip to main content

An Overview of the Black-Scholes-Merton Model After the 2008 Credit Crisis

  • Chapter
  • First Online:
Econometrics of Risk

Part of the book series: Studies in Computational Intelligence ((SCI,volume 583))

  • 2016 Accesses

Abstract

The 2008 credit crisis exposed the over-simplified assumptions of the Black-Scholes-Merton (BSM) model. This paper provides an overview of some of the adjustments forced on the BSM model by the 2008 credit crisis to maintain the relevance of the model. The inclusion of credit value adjustment (CVA), debit value adjustment (DVA), funding value adjustment (FVA) and the posting of collateral in the BSM model are discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Alexander, C.: Quantitative Methods in Finance, Market Risk Analysis, vol. 1. Wiley, Hoboken (2008)

    Google Scholar 

  2. Bergman, Y.Z.: Option pricing with differential interest rates. Rev. Financ. Stud. 8, 475–500 (1995)

    Article  Google Scholar 

  3. Black, F., Scholes, M.: The pricing of options and corporate liabilities. J. Polit. Econ. 81, 637–654 (1973)

    Article  Google Scholar 

  4. Brigo, D., Capponi, A.: Bilateral counterparty risk valuation with stochastic dynamical models and application to CDSs, SSRN working paper (2008)

    Google Scholar 

  5. Brigo, D., Perini, D., Pallavicini, A.: Funding, collateral and hedging: uncovering the mechanics and the subtleties of funding valuation adjustments, SSRN working paper (2011)

    Google Scholar 

  6. Burgard, C., Kjaer, M.: Partial differential equation representations of derivatives with bilateral counterparty risk and funding costs. J. Credit Risk 7, 75–93 (2011)

    Google Scholar 

  7. Burgard, C., Kjaer, M.: Generalised CVA with funding and collateral via semi-replication, SSRN working paper (2012)

    Google Scholar 

  8. Carver, L.: Show me the money: banks explore DVA hedging. Risk Mag. 25, 35–37 (2012)

    Google Scholar 

  9. Castagna, A.: Yes, FVA is a cost for derivatives desks, SSRN working paper, IASON  Ltd (2012)

    Google Scholar 

  10. Cox, J., Ross, S., Rubinstein, M.: Option pricing: a simplified approach. J. Financ. Econ. 7, 229–263 (1979)

    Article  MATH  Google Scholar 

  11. Crépey, S.: Bilateral counterparty risk under funding constraints part I: pricing, forthcoming in Mathematical Finance (2012)

    Google Scholar 

  12. Crépey, S.: Bilateral counterparty risk under funding constraints Part II: CVA, Forthcoming in Mathematical Finance (2012)

    Google Scholar 

  13. Duffie, D., Huang, M.: Swap rates and credit quality. J. Financ. 51, 921–950 (1996)

    Article  Google Scholar 

  14. Gregory, J.: Being two faced over counterparty credit risk. Risk 20, 86–90 (2009)

    Google Scholar 

  15. Gregory, J.: Counterparty Credit Risk and Credit Value Adjustment—A Continuing Challenge for Global Financial Markets, 2nd edn. Wiley, London (2012)

    Book  Google Scholar 

  16. Gregory, J., German, I.: Closing out DVA? SSRN working paper, Barclays, London (2012)

    Google Scholar 

  17. Harrison, M., Pliska, S.: Martingales and stochastic integrals in the theory of continuous trading, stochastic processes and their applications. Stoch. Process. Appl. 11, 215–260 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  18. Hull, J.: Options, Futures, and Other Derivatives, Harlow 8th edn. Pearson Education Limited, Upper Saddle River (2012)

    Google Scholar 

  19. Hull, J., White, A.: The FVA debate. Risk (25th anniversary edition) (2012)

    Google Scholar 

  20. Hull, J., White, A.: The FVA debate continued. Risk 10 (2012)

    Google Scholar 

  21. Hull, J., White, A.: LIBOR versus OIS: the derivatives discounting dilemma. J. Invest. Manag. 11, 14–27 (2013)

    Google Scholar 

  22. Hull, J., White, A.: Collateral and credit issues in derivatives pricing, SSRN working paper (2013)

    Google Scholar 

  23. Hunzinger, C., Labuschagne, C.C.A.: The Cox, Ross and Rubinstein tree model which includes counterparty credit risk and funding costs. N. Am. J. Econ. Financ. 29, 200–217 (2014)

    Article  Google Scholar 

  24. Jarrow, R., Turnbull, S.: Pricing options on financial securities subject to default risk. J. Financ. 1, 53–86 (1995)

    Article  Google Scholar 

  25. Laughton, S., Vaisbrot, A.: In defense of FVA—a response to Hull and White. Risk 25, 18–24 (2012)

    Google Scholar 

  26. Merton, R.: Theory of rational option pricing. Bell. J. Econ. Manag. Sci. 4, 141–183 (1973)

    Article  MathSciNet  Google Scholar 

  27. Piterbarg, V.: Funding beyond discounting: collateral agreements and derivatives pricing, Risk Mag. 97–102 (2010)

    Google Scholar 

  28. Rubinstein, M., Cox, J.C.: Options Market, 1st edn. Prentice-Hall, New York (1985)

    Google Scholar 

  29. Sorensen, E., Bollier, T.: Pricing swap default risk. Financ. Anal. J. 50, 23–33 (1994)

    Article  Google Scholar 

  30. Steland, A.: Financial Statistics and Mathematical Finance Methods, Models and Applications. Wiley, Singapore (2012)

    Book  MATH  Google Scholar 

Download references

Acknowledgments

The authors would like to thank Carlous Reinecke for the helpful discussions. The second named author was supported by the NRF (Grant Number 87502).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Coenraad C. A. Labuschagne .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Hunzinger, C.B., Labuschagne, C.C.A. (2015). An Overview of the Black-Scholes-Merton Model After the 2008 Credit Crisis. In: Huynh, VN., Kreinovich, V., Sriboonchitta, S., Suriya, K. (eds) Econometrics of Risk. Studies in Computational Intelligence, vol 583. Springer, Cham. https://doi.org/10.1007/978-3-319-13449-9_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-13449-9_3

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-13448-2

  • Online ISBN: 978-3-319-13449-9

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics