Uncertainty Quantification and Heston Model

  • María Suárez-Taboada
  • Jeroen A. S. Witteveen
  • Lech A. Grzelak
  • Cornelis W. Oosterlee
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 26)


In this paper, we study the impact of the parameters involved in Heston model by means of Uncertainty Quantification. The Stochastic Collocation Method already used for example in computational fluid dynamics, has been applied throughout this work in order to compute the propagation of the uncertainty from the parameters of the model to the output. The well-known Heston model is considered introduced and parameters involved in the Feller condition are taken as uncertain due to their important influence on the output. Numerical results where the Feller condition is satisfied or not are shown as well as a numerical example with real market data.



This paper has been ERCIM “Alain Bensoussan Fellowship Programme” and partially funded by MCINN (Project MTM2010–21135–C02-01)


  1. 1.
    Achdou, I., Pironneau O.: Computational Methods for Option Pricing. SIAM, Philadelphia (2005)CrossRefzbMATHGoogle Scholar
  2. 2.
    Fang F., Oosterlee C.W.: A novel pricing method for european options based on fourier-cosine series expansions. SIAM J. Sci. Comput. 31, 826–848 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Fang, F., Oosterlee C.W.: Pricing early-exercise and discrete-barrier options by Fourier-cosine series expansions. Numer. Math. 114, 27–62 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Glasserman, P.: Monte Carlo Methods in Financial Engineering. Springer, Berlin (2003)CrossRefzbMATHGoogle Scholar
  5. 5.
    Heston, S.: A closed-form solution for options with stochastic volatility with applications to bond and currency options. Rev. Financ. Stud. 6, 327–343 (1993)CrossRefGoogle Scholar
  6. 6.
    Loeven, G.J.A., Witteveen Jeroen, A.S., Bijl, H.: Probabilistic collocation: an efficient nonintrusive approach for arbitrarily distributed parametric uncertainties. In: 45th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada (2007)Google Scholar
  7. 7.
    Marcozzi, M.D.: On the valuation of Asian options by variational methods. SIAM J. Sci. Comput. 24(4), 1124–1140 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Nobile, F., Tempone, R., Webster, C.G.: A sparse grid stochastic collocation method for partial differential equations with random input data. SIAM J. Sci. Numer. Anal. 46, 2309–2345 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Smolyak, S.A.: Quadrature and interpolation formulas for tensor products of certain classes of functions, Dokl. Akad. Nauk SSSR 4, 240–243 (1963)zbMATHGoogle Scholar
  10. 10.
    Xiu, D., Hesthaven, J.S.: High order collocation methods for differential equations with random inputs. SIAM J. Sci. Comput. 27, 1118–1139 (2005)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2017

Authors and Affiliations

  • María Suárez-Taboada
    • 1
  • Jeroen A. S. Witteveen
  • Lech A. Grzelak
    • 2
  • Cornelis W. Oosterlee
    • 2
  1. 1.Department of MathematicsUniversity of A CoruñaA CoruñaSpain
  2. 2.Delft University of Technology, DIAMDelftNetherlands

Personalised recommendations