Skip to main content

Large Investor Trading Impacts on Volatility

  • Chapter

Part of the Lecture Notes in Mathematics book series (LNM,volume 1919)

This is the first paper in a series devoted to a tentative model for the influence of hedging on the dynamics of an asset. We study here the case of a “large” investor and solve two problems in the context of such a model: the question of the fair value (or liquidation value) of a “large” position and the question of pricing or hedging an option. In order to do so, we use a utility maximization approach and some new results in stochastic control theory.

Keywords

  • Viscosity Solution
  • Option Price
  • Price Dynamic
  • Stochastic Control
  • Stochastic Control Problem

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (Canada)
  • Compact, lightweight 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M. Avellaneda and M.D. Lipkin: A market induced mechanism for stock pinning. (preprint)

    Google Scholar 

  2. K. Back: Insider trading in continuous time. Review of Financial Studies, 5 (1992) 387-409.

    CrossRef  Google Scholar 

  3. K. Back, C.H. Cao and G. Willard: Imperfect condition among informed traders. J. Finance, LV (2000) 2117-2155.

    CrossRef  Google Scholar 

  4. M. Bardi and I. Capuzzo-Dolcetta: Optimal control and viscosity solutions of HamiltonJacobi-Bellman equations. Birkhäusser, Boston (1997).

    CrossRef  Google Scholar 

  5. F. Black and M. Scholes: The pricing of options and corporate liabilities. J. Political Economy, 81 (1973) 637-659.

    CrossRef  Google Scholar 

  6. G. Constantinides and Th. Zariphopoulou: Bounds on prices of contingent claims in an intertemporal economy with proportional transaction costs and general preferences. Finance Stoch., 3 (1999) 345-369.

    CrossRef  MATH  MathSciNet  Google Scholar 

  7. W.H. Fleming and M.H. Soner: Controlled Markow processes and Viscosity Solutions. Springer, Berlin (1993).

    Google Scholar 

  8. H. Föllmer: Stock price fluctuation as a diffusion in a random environment. In Mathematical Models in Finance, eds. S.D. Howison, F.P. Kelly and P. Wilmott, Chapman Hall, London (1995).

    Google Scholar 

  9. R. Frey and A. Stremme: Portfolio insurance and volatility. Department of Economics, Univ. of Bonn (Discussion paper B-256).

    Google Scholar 

  10. A.S. Kyle: Continuous auctions and insider trading. Econometrica, 53 (1985) 1315-1335.

    CrossRef  MATH  Google Scholar 

  11. J.-M. Lasry and P.-L. Lions: Towards a self-consistent theory of volatility. (preprint)

    Google Scholar 

  12. J.-M. Lasry and P.-L. Lions: Une classe nouvelle de problèmes singuliers de contrôle stochastique. C.R. Acad. Sci. Paris, 331 (2000) 879-885.

    MATH  MathSciNet  Google Scholar 

  13. G. Lasserre: Asymmetric information and imperfect competition in a continuous time multivariate secutiry model. Finance and Stochastics, 8 (2004) 285-309.

    CrossRef  MATH  MathSciNet  Google Scholar 

  14. R. Merton: Theory of rational option pricing. Bull. J. Econom. Manag. Sci., 4 (1973) 141-183.

    CrossRef  MathSciNet  Google Scholar 

  15. M. Musiela and Th. Zariphopoulou: Indifference prices and related measures. (preprint)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and Permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Lions, PL., Lasry, JM. (2007). Large Investor Trading Impacts on Volatility. In: Paris-Princeton Lectures on Mathematical Finance 2004. Lecture Notes in Mathematics, vol 1919. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73327-0_4

Download citation