Preliminary remarks on option pricing and dynamic hedging

Michel Fliess (1) , Cédric Join (2, 3)

1 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
2 ALIEN - Algebra for Digital Identification and Estimation
3 CRAN - Centre de Recherche en Automatique de Nancy

An elementary arbitrage principle and the existence of trends in financial time series, which is based on a theorem published in 1995 by P. Cartier and Y. Perrin, lead to a new understanding of option pricing and dynamic hedging. Intricate problems related to violent behaviors of the underlying, like the existence of jumps, become then quite straightforward by incorporating them into the trends. Several convincing computer experiments are reported.

Keywords: Quantitative finance; option pricing; European option; dynamic hedging; replication; arbitrage; time series; trends; volatility; abrupt changes; model-free control; nonstandard analysis; nonstandard analysis.

Domains: Computational Finance [q-fin.CP]; Risk Management [q-fin.RM]; Logic [math.LO]; Probability [math.PR]; Statistics [math.ST]; Statistics Theory [stat.TH]; Automatic Control Engineering; Signal and Image Processing; Signal and Image processing

Michel Fliess, Cédric Join. Preliminary remarks on option pricing and dynamic hedging. 1st International Conference on Systems and Computer Science, Aug 2012, Villeneuve d'Ascq, France. pp.CDROM. ⟨hal-00705373⟩