Advertisement

Utility-Based Valuation and Hedging of Derivatives

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

Abstract

Valuation based on quadratic hedging is easy to understand and mathematically tractable compared to other approaches. Its economic justification is less obvious.

References

  1. 4.
    P. Artzner, F. Delbaen, J. Eber, D. Heath, Coherent measures of risk. Math. Finance 9(3), 203–228 (1999)MathSciNetCrossRefGoogle Scholar
  2. 11.
    P. Barrieu, N. El Karoui, Optimal derivatives design under dynamic risk measures, in Mathematics of Finance, vol. 351 (Amer. Math. Soc., Providence, 2004), pp. 13–25zbMATHGoogle Scholar
  3. 12.
    P. Barrieu, N. El Karoui, Inf-convolution of risk measures and optimal risk transfer. Finance Stochast. 9(2), 269–298 (2005)MathSciNetCrossRefGoogle Scholar
  4. 19.
    D. Becherer, Rational hedging and valuation of integrated risks under constant absolute risk aversion. Insurance Math. Econom. 33(1), 1–28 (2003)MathSciNetCrossRefGoogle Scholar
  5. 20.
    D. Becherer, Bounded solutions to backward SDE’s with jumps for utility optimization and indifference hedging. Ann. Appl. Probab. 16(4), 2027–2054 (2006)MathSciNetCrossRefGoogle Scholar
  6. 25.
    S. Biagini, M. Frittelli, M. Grasselli, Indifference price with general semimartingales. Math. Finance 21(3), 423–446 (2011)MathSciNetCrossRefGoogle Scholar
  7. 45.
    R. Carmona (ed.), Indifference Pricing: Theory and Applications (Princeton Univ. Press, Princeton, 2009)zbMATHGoogle Scholar
  8. 74.
    F. Delbaen, P. Grandits, T. Rheinländer, D. Samperi, M. Schweizer, C. Stricker, Exponential hedging and entropic penalties. Math. Finance 12(2), 99–123 (2002)MathSciNetCrossRefGoogle Scholar
  9. 116.
    H. Föllmer, A. Schied, Convex measures of risk and trading constraints. Finance Stochast. 6(4), 429–447 (2002)MathSciNetCrossRefGoogle Scholar
  10. 117.
    H. Föllmer, A. Schied, Stochastic Finance: An Introduction in Discrete Time, 3rd edn. (De Gruyter, Berlin, 2011)CrossRefGoogle Scholar
  11. 121.
    M. Frittelli, E. Rosazza Gianin, Putting order in risk measures. J. Bank. Financ. 26(7), 1473–1486 (2002)CrossRefGoogle Scholar
  12. 139.
    D. Heath, H. Ku, Pareto equilibria with coherent measures of risk. Math. Finance 14(2), 163–172 (2004)MathSciNetCrossRefGoogle Scholar
  13. 141.
    V. Henderson, Valuation of claims on nontraded assets using utility maximization. Math. Finance 12(4), 351–373 (2002)MathSciNetCrossRefGoogle Scholar
  14. 145.
    S. Hodges, A. Neuberger, Optimal replication of contingent claims under transaction costs. Rev. Futur. Mark. 8, 222–239 (1989)Google Scholar
  15. 164.
    J. Kallsen, A utility maximization approach to hedging in incomplete markets. Math. Methods Oper. Res. 50(2), 321–338 (1999)MathSciNetCrossRefGoogle Scholar
  16. 166.
    J. Kallsen, Derivative pricing based on local utility maximization. Finance Stochast. 6(1), 115–140 (2002)MathSciNetCrossRefGoogle Scholar
  17. 180.
    J. Kallsen, T. Rheinländer, Asymptotic utility-based pricing and hedging for exponential utility. Stat. Decis. 28(1), 17–36 (2011)MathSciNetzbMATHGoogle Scholar
  18. 198.
    D. Kramkov, M. Sîrbu, Sensitivity analysis of utility-based prices and risk-tolerance wealth processes. Ann. Appl. Probab. 16(4), 2140–2194 (2006)MathSciNetCrossRefGoogle Scholar
  19. 199.
    D. Kramkov, M. Sîrbu, Asymptotic analysis of utility-based hedging strategies for small number of contingent claims. Stoch. Process. Appl. 117(11), 1606–1620 (2007)MathSciNetCrossRefGoogle Scholar
  20. 211.
    D. Madan, P. Carr, E. Chang, The variance gamma process and option pricing. Eur. Finance Rev. 2(1), 79–105 (1998)CrossRefGoogle Scholar
  21. 212.
    M. Mania, M. Schweizer, Dynamic exponential utility indifference valuation. Ann. Appl. Probab. 15(3), 2113–2143 (2005)MathSciNetCrossRefGoogle Scholar
  22. 216.
    A. McNeil, R. Frey, P. Embrechts, Quantitative Risk Management: Concepts, Techniques and Tools, 2nd edn. (Princeton Univ. Press, Princeton, 2015)zbMATHGoogle Scholar
  23. 242.
    T. Rheinländer, J. Sexton, Hedging Derivatives (World Scientific, Hackensack, 2011)CrossRefGoogle Scholar
  24. 253.
    R. Rouge, N. El Karoui, Pricing via utility maximization and entropy. Math. Finance 10(2), 259–276 (2000)MathSciNetCrossRefGoogle Scholar
  25. 286.
    A. Toussaint, R. Sircar, A framework for dynamic hedging under convex risk measures. Seminar on Stochastic Analysis, Random Fields and Applications VI (Birkhäuser, Basel, 2011), pp. 429–451CrossRefGoogle 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