Delta Hedging in Financial Engineering: Towards a Model-Free Approach
AbstractDelta hedging, which plays a crucial rôle in modern financial engineering, is a tracking control design for a "risk-free" management. We utilize the existence of trends in financial time series (Fliess M., Join C.: A mathematical proof of the existence of trends in financial time series, Proc. Int. Conf. Systems Theory: Modelling, Analysis and Control, Fes, 2009. Online: http://hal.inria.fr/inria-00352834/en/) in order to propose a model-free setting for delta hedging. It avoids most of the shortcomings encountered with the now classic Black-Scholes-Merton framework. Several convincing computer simulations are presented. Some of them are dealing with abrupt changes, i.e., jumps.
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Date of creation: 23 Jun 2010
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Publication status: Published - Presented, 18th Mediterranean Conference on Control and Automation, MED'10, 2010, Marrakech, Morocco
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Financial engineering; delta hedging; dynamic hedging; trends; quick fluctuations; abrupt changes; jumps; tracking control; model-free control;
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- Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
- Michel Fliess & C\'edric Join, 2009. "A mathematical proof of the existence of trends in financial time series," Papers 0901.1945, arXiv.org.
- Michel Fliess & Cédric Join & Mamadou Mboup, 2010. "Algebraic change-point detection," Post-Print inria-00439226, HAL.
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