Skip to main content

From Model to Application: Calibration to Market Data

  • Chapter
FPGA Based Accelerators for Financial Applications
  • 2460 Accesses

Abstract

We present the procedure of model calibration within the scope of financial applications. We discuss several models that are used to describe the movement of financial underlyings and state closed or semi-closed pricing formulas for basic financial instruments. Furthermore, we explain how these are used in a general calibration procedure with the purpose to determine sensible model parameters. Finally, we gather typical numerical issues that often arise in the context of calibration and that have to be handled with care.

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 79.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 99.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 139.99
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. Bakshi, G., Cao, C., Chen, Z.: Empirical performance of alternative option pricing models. J. Financ. 52(5), 2003–2049 (1997)

    Article  Google Scholar 

  2. Bates, D.S.: Jumps and stochastic volatility: exchange rate processes implicit in deutsche mark options. Rev. Financ. Stud. 9(1), 69–107 (1996)

    Article  Google Scholar 

  3. Black, F.: The pricing of commodity contracts. J. Financ. Econ. 3(1), 167–179 (1976)

    Article  Google Scholar 

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

    Article  Google Scholar 

  5. Brigo, D., Mercurio, F.: Interest Rate Models – Theory and Practice: With Smile, Inflation and Credit. Springer Finance, 2nd edn. Springer, Berlin/New York (2006)

    Google Scholar 

  6. Brugger, C., Liu, G., de Schryver, C., Wehn, N.: A systematic methodology for analyzing closed-form Heston pricer regarding their accuracy and runtime. In: Proceedings of the 7th Workshop on High Performance Computational Finance, pp. 9–16. IEEE (2014), New Orleans, Louisiana, USA

    Google Scholar 

  7. Carr, P., Madan, D.: Option valuation using the fast Fourier transform. J. Comput. Financ. 2, 61–73 (1999)

    Google Scholar 

  8. Cody, W.J.: Rational Chebyshev approximations for the error function. Math. Comput. 23(107), 631–637 (1969)

    Article  MathSciNet  MATH  Google Scholar 

  9. Dimitroff, G., Lorenz, S., Szimayer, A.: A parsimonious multi-asset Heston model: calibration and derivative pricing. Int. J. Theor. Appl. Financ. 14(8), 1299–1333 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  10. Gatheral, J.: The Volatility Surface: A Practitioner’s Guide. Wiley, Hoboken (2006)

    Google Scholar 

  11. Hadamard, J.: Lectures on Cauchy’s Problem in Linear Partial Differential Equations. Yale University Press, New Haven (1923)

    MATH  Google Scholar 

  12. Hagan, P., Kumar, D., Lesniewski, A., Woodward, D.: Managing smile risk. Wilmott Mag. 84–108 (2002)

    Google Scholar 

  13. Heston, S.L.: A closed-form solution for options with stochastic volatility with applications to bond and currency options. Rev. Financ. Stud. 6(2), 327–343 (1993)

    Article  Google Scholar 

  14. Hirsa, A., Neftci, S.N.: An Introduction to the Mathematics of Financial Derivatives. Academic, London (2013)

    MATH  Google Scholar 

  15. Korn, R., Korn, E.: Option Pricing and Portfolio Optimization: Modern Methods of Financial Mathematics. American Mathematical Society, Providence (2001)

    Book  Google Scholar 

  16. Korn, R., Korn, E., Kroisandt, G.: Monte Carlo Methods and Models in Finance and Insurance. Chapman & Hall/CRC Financial Mathematics Series. CRC, London (2010)

    Book  MATH  Google Scholar 

  17. Lindström, E., Ströjby, J., Brodén, M., Wiktorsson, M., Holst, J.: Sequential calibration of options. Comput. Stat. Data Anal. 52(6), 2877–2891 (2008)

    Article  MATH  Google Scholar 

  18. Merton, R.C.: Option Pricing when underlying Stock Returns are discontinuous. J. Financ. Econ. 3(1–2), 125–144 (1976)

    Article  MATH  Google Scholar 

  19. Mikhailov, S., Nögel, U.: Heston’s stochastic volatility model: implementation, calibration and some extensions. Wilmott Mag. (2003) 74–79

    Google Scholar 

  20. Schoutens, W., Simons, E., Tistaert, J.: A perfect calibration! Now what? Wilmott Mag. 66–78 (2004)

    Google Scholar 

  21. Tikhonov, A.N., Arsenin, V.Y.: Solutions of Ill-Posed Problems. Wiley, New York (1977)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Tilman Sayer .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Sayer, T., Wenzel, J. (2015). From Model to Application: Calibration to Market Data. In: De Schryver, C. (eds) FPGA Based Accelerators for Financial Applications. Springer, Cham. https://doi.org/10.1007/978-3-319-15407-7_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-15407-7_2

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-15406-0

  • Online ISBN: 978-3-319-15407-7

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics