Optimal hedging of derivatives with transaction costs
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
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.
Black and Scholes, Growth optimal criteria, Transaction costs
Computer and Information Science
IdentifiersURN: urn:nbn:se:kth:diva-55905DOI: 10.1142/S0219024906003901ScopusID: 2-s2.0-33751067199OAI: oai:DiVA.org:kth-55905DiVA: diva2:472119
QC 201201102012-01-032012-01-032012-01-10Bibliographically approved