Equity Models

  • Ernst Eberlein
  • Jan Kallsen
Part of the Springer Finance book series (FINANCE)


The theory of Mathematical Finance in the following chapters rests on price processes of assets such as stocks, currencies, bonds, and commodities. They are often assumed to be given exogenously. Therefore we start by discussing what kinds of processes are suggested by statistical properties of real data.


  1. 5.
    L. Bachelier, Théorie de la Spéculation (Gauthier-Villars, Paris, 1900)CrossRefGoogle Scholar
  2. 10.
    O. Barndorff-Nielsen, N. Shephard, Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics. J. R. Stat. Soc. Ser. B Stat. Methodol. 63(2), 167–241 (2001)MathSciNetCrossRefGoogle Scholar
  3. 15.
    D. Bates, Jumps and stochastic volatility: Exchange rate processes implicit in deutsche mark options. Rev. Financ. Stud. 9(1), 69–107 (1996)CrossRefGoogle Scholar
  4. 49.
    P. Carr, L. Wu, The finite moment log stable process and option pricing. J. Finance 58(2), 753–778 (2003)CrossRefGoogle Scholar
  5. 50.
    P. Carr, L. Wu, Time-changed Lévy processes and option pricing. J. Financ. Econ. 71(1), 113–141 (2004)CrossRefGoogle Scholar
  6. 52.
    P. Carr, H. Geman, D. Madan, M. Yor, Stochastic volatility for Lévy processes. Math. Finance 13(3), 345–382 (2003)MathSciNetCrossRefGoogle Scholar
  7. 60.
    R. Cont, P. Tankov, Financial Modelling with Jump Processes (Chapman & Hall/CRC, Boca Raton, 2004)Google Scholar
  8. 142.
    S. Heston, A closed-form solution for options with stochastic volatility with applications to bond and currency options. Rev. Financ. Stud. 6(2), 327–343 (1993)MathSciNetCrossRefGoogle Scholar
  9. 169.
    J. Kallsen, A didactic note on affine stochastic volatility models. From Stochastic Calculus to Mathematical Finance (Springer, Berlin, 2006), pp. 343–368CrossRefGoogle Scholar
  10. 183.
    J. Kallsen, P. Tankov, Characterization of dependence of multidimensional Lévy processes using Lévy copulas. J. Multivariate Anal. 97(7), 1551–1572 (2006)MathSciNetCrossRefGoogle Scholar
  11. 228.
    M. Osborne, Brownian motion in the stock market. Oper. Res. 7(2), 145–173 (1959)MathSciNetCrossRefGoogle Scholar
  12. 231.
    A. Pauwels, Variance-Optimal Hedging in Affine Volatility Models. PhD thesis, Technical University of Munich, 2007Google Scholar
  13. 257.
    P. Samuelson, Rational theory of warrant pricing. Ind. Manag. Rev. 6(2), 13 (1965)Google Scholar
  14. 261.
    R. Schöbel, J. Zhu, Stochastic volatility with an Ornstein–Uhlenbeck process: an extension. Eur. Finance Rev. 3(1), 23–46 (1999)CrossRefGoogle Scholar
  15. 263.
    W. Schoutens, Lévy Processes in Finance (Wiley, New York, 2003)CrossRefGoogle Scholar
  16. 280.
    E. Stein, J. Stein, Stock price distributions with stochastic volatility: an analytic approach. Rev. Financ. Stud. 4(4), 727–752 (1991)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Ernst Eberlein
    • 1
  • Jan Kallsen
    • 2
  1. 1.Department of Mathematical StochasticsUniversity of FreiburgFreiburg im BreisgauGermany
  2. 2.Department of MathematicsKiel UniversityKielGermany

Personalised recommendations