OPTIMAL HEDGING OF DERIVATIVES WITH TRANSACTION COSTS

Erik Aurell () and Paolo Muratore-Ginanneschi ()
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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

International Journal of Theoretical and Applied Finance (IJTAF), 2006, vol. 09, issue 07, 1051-1069

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.

Keywords: Growth optimal criteria; transaction costs; Black and Scholes (search for similar items in EconPapers)
Date: 2006
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DOI: 10.1142/S0219024906003901

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