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Optimal Hedging Of Derivatives With Transaction Costs

Author

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  • ERIK AURELL

    (AlbaNova University Center, Department of Physics, KTH — Royal Institute of Technology, SE-106 91, Stockholm, Sweden)

  • PAOLO MURATORE-GINANNESCHI

    (Departments of Mathematics and Statistics, University of Helsinki PL 68, FIN-00014, Helsingin Yliopisto, Finland)

Abstract

We investigate the optimal strategy over a finite time horizon for a portfolio of stock and bond and a derivative in an multiplicative Markovian market model with transaction costs (friction). The optimization problem is solved by a Hamilton–Jacobi–Bellman equation, which by the verification theorem has well-behaved solutions if certain conditions on a potential are satisfied. In the case at hand, these conditions simply imply arbitrage-free ("Black–Scholes") pricing of the derivative. While pricing is hence not changed by friction allow a portfolio to fluctuate around a delta hedge. In the limit of weak friction, we determine the optimal control to essentially be of two parts: a strong control, which tries to bring the stock-and-derivative portfolio towards a Black–Scholes delta hedge; and a weak control, which moves the portfolio by adding or subtracting a Black–Scholes hedge. For simplicity we assume growth-optimal investment criteria and quadratic friction.

Suggested Citation

  • Erik Aurell & Paolo Muratore-Ginanneschi, 2006. "Optimal Hedging Of Derivatives With Transaction Costs," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 9(07), pages 1051-1069.
    • Handle: RePEc:wsi:ijtafx:v:09:y:2006:i:07:n:s0219024906003901
    DOI: 10.1142/S0219024906003901
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    References listed on IDEAS

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    1. J. Doyne Farmer, 2002. "Market force, ecology and evolution," Industrial and Corporate Change, Oxford University Press and the Associazione ICC, vol. 11(5), pages 895-953, November.
    2. Bernard Bensaid & Jean‐Philippe Lesne & Henri Pagès & José Scheinkman, 1992. "Derivative Asset Pricing With Transaction Costs1," Mathematical Finance, Wiley Blackwell, vol. 2(2), pages 63-86, April.
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