Advertisement

Arbitrage-Based Valuation and Hedging of Derivatives

  • Ernst Eberlein
  • Jan Kallsen
Chapter
  • 1.2k Downloads
Part of the Springer Finance book series (FINANCE)

Abstract

The valuation of derivative securities constitutes one of the main issues in modern Mathematical Finance. Economic theory has considered the genesis of asset prices for a long time.

References

  1. 29.
    T. Björk, Arbitrage Theory in Continuous Time, 3rd edn. (Oxford Univ. Press, Oxford, 2009)zbMATHGoogle Scholar
  2. 40.
    D. Breeden, R. Litzenberger, Prices of state-contingent claims implicit in option prices. J. Bus., 621–651 (1978)CrossRefGoogle Scholar
  3. 47.
    P. Carr, R. Lee, Robust replication of volatility derivatives, in PRMIA Award for Best Paper in Derivatives, MFA 2008 Annual Meeting, 2009Google Scholar
  4. 48.
    P. Carr, D. Madan, Option valuation using the fast Fourier transform. J. Comput. Finance 2(4), 61–73 (1999)CrossRefGoogle Scholar
  5. 53.
    P. Carr, R. Lee, L. Wu, Variance swaps on time-changed Lévy processes. Finance Stochast. 16(2), 335–355 (2012)zbMATHCrossRefGoogle Scholar
  6. 59.
    R. Cont, Model uncertainty and its impact on the pricing of derivative instruments. Math. Finance 16(3), 519–547 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 60.
    R. Cont, P. Tankov, Financial Modelling with Jump Processes (Chapman & Hall/CRC, Boca Raton, 2004)Google Scholar
  8. 69.
    M. Davis, Complete-market models of stochastic volatility. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 460(2041), 11–26 (2004)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 70.
    F. Delbaen, W. Schachermayer, A general version of the fundamental theorem of asset pricing. Math. Ann. 300(3), 463–520 (1994)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 71.
    F. Delbaen, W. Schachermayer, The Banach space of workable contingent claims in arbitrage theory. Ann. Inst. H. Poincaré Probab. Statist. 33(1), 113–144 (1997)MathSciNetzbMATHCrossRefGoogle Scholar
  11. 72.
    F. Delbaen, W. Schachermayer, The fundamental theorem of asset pricing for unbounded stochastic processes. Math. Ann. 312(2), 215–250 (1998)MathSciNetzbMATHCrossRefGoogle Scholar
  12. 73.
    F. Delbaen, W. Schachermayer, The Mathematics of Arbitrage (Springer, Berlin, 2006)zbMATHGoogle Scholar
  13. 81.
    E. Eberlein, J. Jacod, On the range of options prices. Finance Stochast. 1(2), 131–140 (1997)zbMATHCrossRefGoogle Scholar
  14. 92.
    E. Eberlein, K. Glau, A. Papapantoleon, Analysis of Fourier transform valuation formulas and applications. Appl. Math. Finance 17(3), 211–240 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  15. 93.
    E. Eberlein, K. Glau, A. Papapantoleon, Analyticity of the Wiener-Hopf factors and valuation of exotic options in Lévy models, in Advanced Mathematical Methods for Finance (Springer, Heidelberg, 2011), pp. 223–245zbMATHGoogle Scholar
  16. 97.
    N. El Karoui, M. Jeanblanc-Picqué, S. Shreve, Robustness of the Black and Scholes formula. Math. Finance 8(2), 93–126 (1998)MathSciNetzbMATHCrossRefGoogle Scholar
  17. 101.
    F. Fang, C. Oosterlee, A novel pricing method for European options based on Fourier-cosine series expansions. SIAM J. Sci. Comput. 31(2), 826–848 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  18. 120.
    R. Frey, C. Sin, Bounds on European option prices under stochastic volatility. Math. Finance 9(2), 97–116 (1999)MathSciNetzbMATHCrossRefGoogle Scholar
  19. 122.
    H. Geman, N. El Karoui, J. Rochet, Changes of numéraire, changes of probability measure and option pricing. J. Appl. Probab. 32(2), 443–458 (1995)MathSciNetzbMATHCrossRefGoogle Scholar
  20. 123.
    P. Glasserman, Monte Carlo Methods in Financial Engineering (Springer, New York, 2004)zbMATHGoogle Scholar
  21. 133.
    M. Harrison, S. Pliska, Martingales and stochastic integrals in the theory of continuous trading. Stoch. Process. Appl. 11(3), 215–260 (1981)MathSciNetzbMATHCrossRefGoogle Scholar
  22. 134.
    M. Harrison, S. Pliska, A stochastic calculus model of continuous trading: complete markets. Stoch. Process. Appl. 15(3), 313–316 (1983)MathSciNetzbMATHCrossRefGoogle Scholar
  23. 143.
    N. Hilber, O. Reichmann, C. Schwab, and C. Winter. Computational Methods for Quantitative Finance: Finite Element Methods for Derivative Pricing (Springer, Heidelberg, 2013)zbMATHCrossRefGoogle Scholar
  24. 147.
    F. Hubalek, J. Kallsen, Variance-optimal hedging and Markowitz-efficient portfolios for multivariate processes with stationary independent increments with and without constraints (2004). preprintGoogle Scholar
  25. 148.
    F. Hubalek, J. Kallsen, L. Krawczyk, Variance-optimal hedging for processes with stationary independent increments. Ann. Appl. Probab. 16(2), 853–885 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  26. 150.
    S. Jacka, A martingale representation result and an application to incomplete financial markets. Math. Finance 2(4), 239–250 (1992)zbMATHCrossRefGoogle Scholar
  27. 171.
    J. Kallsen, C. Kühn, Convertible bonds: financial derivatives of game type. Exotic Option Pricing and Advanced Lévy Models (Wiley, Chichester, 2005), pp. 277–291Google Scholar
  28. 196.
    D. Kramkov, Optional decomposition of supermartingales and hedging contingent claims in incomplete security markets. Probab. Theory Relat. Fields 105(4), 459–479 (1996)MathSciNetzbMATHCrossRefGoogle Scholar
  29. 204.
    D. Lamberton, B. Lapeyre, Stochastic Calculus Applied to Finance (Chapman & Hall, London, 1996)zbMATHGoogle Scholar
  30. 219.
    R. Merton, Theory of rational option pricing. Bell J. Econom. Manag. Sci. 4, 141–183 (1973)MathSciNetzbMATHCrossRefGoogle Scholar
  31. 240.
    S. Raible, Lévy Processes in Finance: Theory, Numerics, and Empirical Facts. PhD thesis, University of Freiburg, 2000Google Scholar
  32. 264.
    W. Schoutens, E. Simons, J. Tistaert, A perfect calibration! Now what? Wilmott Magazine 2004, 66–78 (2004)CrossRefGoogle Scholar
  33. 265.
    K. Schürger, Laplace transforms and suprema of stochastic processes. Advances in Finance and Stochastics (Springer, Berlin, 2002), pp. 285–294zbMATHCrossRefGoogle Scholar
  34. 272.
    R. Seydel, Tools for Computational Finance, 4th edn. (Springer, Berlin, 2009)zbMATHGoogle Scholar
  35. 279.
    S. Shreve, Stochastic Calculus for Finance II: Continuous-Time Models (Springer, New York, 2004)zbMATHCrossRefGoogle Scholar
  36. 281.
    C. Stricker, Arbitrage et lois de martingale. Ann. Inst. H. Poincaré Probab. Stat. 26(3), 451–460 (1990)MathSciNetzbMATHGoogle Scholar
  37. 285.
    M. Taqqu, W. Willinger, The analysis of finite security markets using martingales. Adv. Appl. Probab. 19(1), 1–25 (1987)MathSciNetzbMATHCrossRefGoogle Scholar
  38. 293.
    J. Xia, J. Yan, A new look at some basic concepts in arbitrage pricing theory. Sci. China Ser. A 46(6), 764–774 (2003)MathSciNetzbMATHCrossRefGoogle Scholar
  39. 294.
    J. Yan, A new look at the fundamental theorem of asset pricing. J. Korean Math. Soc. 35(3), 659–673 (1998). International Conference on Probability Theory and Its Applications (Taejon, 1998)Google 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