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Hedging Options: The Malliavin Calculus Approach versus the Δ‐Hedging Approach

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  • Hans‐Peter Bermin

Abstract

In this paper we consider a Black and Scholes economy and investigate two approaches to hedging contingent claims. We show that the general Malliavin calculus approach can generate the classical Δ‐hedging formula under weaker conditions.

Suggested Citation

  • Hans‐Peter Bermin, 2003. "Hedging Options: The Malliavin Calculus Approach versus the Δ‐Hedging Approach," Mathematical Finance, Wiley Blackwell, vol. 13(1), pages 73-84, January.
    • Handle: RePEc:bla:mathfi:v:13:y:2003:i:1:p:73-84
    DOI: 10.1111/1467-9965.t01-1-00006
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    References listed on IDEAS

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    1. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
    2. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    3. Jan Ubøe & Bernt Øksendal & Knut Aase & Nicolas Privault, 2000. "White noise generalizations of the Clark-Haussmann-Ocone theorem with application to mathematical finance," Finance and Stochastics, Springer, vol. 4(4), pages 465-496.
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    Cited by:

    1. Elisa Alòs & Christian-Olivier Ewald, 2005. "A note on the Malliavin differentiability of the Heston volatility," Economics Working Papers 880, Department of Economics and Business, Universitat Pompeu Fabra.
    2. Doriana Ruffino, 2014. "Resuscitating Businessman Risk: A Rationale for Familiarity-Based Portfolios," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 17(1), pages 107-130, January.
    3. Amilon, Henrik & Bermin, Hans-Peter, 2003. "Welfare effects of controlling labor supply: an application of the stochastic Ramsey model," Journal of Economic Dynamics and Control, Elsevier, vol. 28(2), pages 331-348, November.

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