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Residual risks and hedging strategies in Markovian markets

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  • Bouleau, Nicolas
  • Lamberton, Damien

Abstract

We prove two explicit formulae for the quadratic residual risk and for the optimal hedging portfolio of a European contingent claim when the underlying stock prices are functions of a Markov process. These expressions allow the practical handling of a great deal of non classical models which are less optimistic than Black and Scholes's one

Suggested Citation

  • Bouleau, Nicolas & Lamberton, Damien, 1989. "Residual risks and hedging strategies in Markovian markets," Stochastic Processes and their Applications, Elsevier, vol. 33(1), pages 131-150, October.
  • Handle: RePEc:eee:spapps:v:33:y:1989:i:1:p:131-150
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    Citations

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    Cited by:

    1. Christian Gourieroux & Jean Paul Laurent & Huyên Pham, 1998. "Mean‐Variance Hedging and Numéraire," Mathematical Finance, Wiley Blackwell, vol. 8(3), pages 179-200, July.
    2. repec:dau:papers:123456789/5374 is not listed on IDEAS
    3. Dirk Becherer & Ian Ward, 2010. "Optimal Weak Static Hedging of Equity and Credit Risk Using Derivatives," Applied Mathematical Finance, Taylor & Francis Journals, vol. 17(1), pages 1-28.
    4. Jean -Luc Prigent & Olivier Renault & Olivier Scaillet, 1999. "An Autoregressive Conditional Binomial Option Pricing Model," Working Papers 99-65, Center for Research in Economics and Statistics.
    5. Ewald, Christian-Oliver & Nawar, Roy & Siu, Tak Kuen, 2013. "Minimal variance hedging of natural gas derivatives in exponential Lévy models: Theory and empirical performance," Energy Economics, Elsevier, vol. 36(C), pages 97-107.
    6. Prigent, Jean-Luc & Renault, Olivier & Scaillet, Olivier, 2004. "Option pricing with discrete rebalancing," Journal of Empirical Finance, Elsevier, vol. 11(1), pages 133-161, January.
    7. Ke Du, 2013. "Commodity Derivative Pricing Under the Benchmark Approach," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 2, July-Dece.
    8. Ke Du, 2013. "Commodity Derivative Pricing Under the Benchmark Approach," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1-2013, January.
    9. Damiano Brigo & Fabio Mercurio, 2008. "Discrete Time vs Continuous Time Stock-price Dynamics and implications for Option Pricing," Papers 0812.4010, arXiv.org.
    10. Nicolas Bouleau, 2013. "The Environmental Violence of Volatility," CIRED Working Papers halshs-00835669, HAL.
    11. Zhang, Xiaolan, 1995. "Formules quasi-explicites pour les options américaines dans un modèle de diffusion avec sauts," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 38(1), pages 151-161.
    12. Mercurio, Fabio, 2001. "Claim pricing and hedging under market incompleteness and "mean-variance" preferences," European Journal of Operational Research, Elsevier, vol. 133(3), pages 635-652, September.
    13. Møller, T., 2002. "On Valuation and Risk Management at the Interface of Insurance and Finance," British Actuarial Journal, Cambridge University Press, vol. 8(4), pages 787-827, October.
    14. Nicolas Bouleau, 2003. "Error Calculus and Path Sensitivity in Financial Models," Mathematical Finance, Wiley Blackwell, vol. 13(1), pages 115-134, January.
    15. repec:dau:papers:123456789/12663 is not listed on IDEAS
    16. Nicolas Bouleau, 2013. "The Environmental Violence of Volatility," Working Papers halshs-00835669, HAL.
    17. Fischer, Tom, 2007. "A law of large numbers approach to valuation in life insurance," Insurance: Mathematics and Economics, Elsevier, vol. 40(1), pages 35-57, January.
    18. Thomson, Robert J., 2005. "The pricing of liabilities in an incomplete market using dynamic mean-variance hedging," Insurance: Mathematics and Economics, Elsevier, vol. 36(3), pages 441-455, June.

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