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Optimal hedging of derivatives with transaction costs
KTH, Skolan för elektro- och systemteknik (EES), Centra, ACCESS Linnaeus Centre. KTH, Skolan för datavetenskap och kommunikation (CSC), Beräkningsbiologi, CB.
Departments of Mathematics and Statistics, University of Helsinki.
2006 (Engelska)Ingår i: International Journal of Theoretical and Applied Finance, ISSN 0219-0249, Vol. 9, nr 7, s. 1051-1069Artikel i tidskrift (Refereegranskat) 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.

Ort, förlag, år, upplaga, sidor
2006. Vol. 9, nr 7, s. 1051-1069
Nyckelord [en]
Black and Scholes, Growth optimal criteria, Transaction costs
Nationell ämneskategori
Data- och informationsvetenskap
Identifikatorer
URN: urn:nbn:se:kth:diva-55905DOI: 10.1142/S0219024906003901Scopus ID: 2-s2.0-33751067199OAI: oai:DiVA.org:kth-55905DiVA, id: diva2:472119
Anmärkning
QC 20120110Tillgänglig från: 2012-01-03 Skapad: 2012-01-03 Senast uppdaterad: 2018-01-12Bibliografiskt granskad

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Aurell, ErikMuratore-Ginnaneschi, Paolo
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ACCESS Linnaeus CentreBeräkningsbiologi, CB
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International Journal of Theoretical and Applied Finance
Data- och informationsvetenskap

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