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Optimal hedging of Derivatives with transaction costs

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  • Erik Aurell
  • Paolo Muratore-Ginanneschi

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-Bellman-Jacobi 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.

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  • Erik Aurell & Paolo Muratore-Ginanneschi, 2005. "Optimal hedging of Derivatives with transaction costs," Papers physics/0509150, arXiv.org, revised Dec 2005.
    • Handle: RePEc:arx:papers:physics/0509150
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    References listed on IDEAS

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    1. Dybvig, Philip H & Rogers, L C G & Back, Kerry, 1999. "Portfolio Turnpikes," The Review of Financial Studies, Society for Financial Studies, vol. 12(1), pages 165-195.
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