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Optimal hedging of derivatives with transaction costs
KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Computer Science and Communication (CSC), Computational Biology, CB.
Departments of Mathematics and Statistics, University of Helsinki.
2006 (English)In: International Journal of Theoretical and Applied Finance, ISSN 0219-0249, Vol. 9, no 7, 1051-1069 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2006. Vol. 9, no 7, 1051-1069 p.
Keyword [en]
Black and Scholes, Growth optimal criteria, Transaction costs
National Category
Computer and Information Science
URN: urn:nbn:se:kth:diva-55905DOI: 10.1142/S0219024906003901ScopusID: 2-s2.0-33751067199OAI: diva2:472119
QC 20120110Available from: 2012-01-03 Created: 2012-01-03 Last updated: 2012-01-10Bibliographically approved

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