A Stieltjes approach to static hedges

Schmutz, Michael; Zürcher, Thomas (2014). A Stieltjes approach to static hedges. In: Kabanov, Yuri; Rutkowski, Marek; Zariphopoulou, Thaleia (eds.) Inspired by Finance - The Musiela Festschrift (pp. 519-534). Switzerland: Springer 10.1007/978-3-319-02069-3_24

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Static hedging of complicated payoff structures by standard instruments becomes increasingly popular in finance. The classical approach is developed for quite regular functions, while for less regular cases, generalized functions and approximation arguments are used. In this note, we discuss the regularity conditions in the classical decomposition formula due to P. Carr and D. Madan (in Jarrow ed, Volatility, pp. 417–427, Risk Publ., London, 1998) if the integrals in this formula are interpreted as Lebesgue integrals with respect to the Lebesgue measure. Furthermore, we show that if we replace these integrals by Lebesgue–Stieltjes integrals, the family of representable functions can be extended considerably with a direct approach.

Item Type:	Book Section (Book Chapter)
Division/Institute:	08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics 08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematical Statistics and Actuarial Science
UniBE Contributor:	Schmutz, Michael, Zürcher, Thomas
Subjects:	500 Science > 510 Mathematics
ISBN:	978-3-319-02069-3
Publisher:	Springer
Language:	English
Submitter:	Lutz Dümbgen
Date Deposited:	01 Apr 2014 03:08
Last Modified:	05 Dec 2022 14:28
Publisher DOI:	10.1007/978-3-319-02069-3_24
URI:	https://boris.unibe.ch/id/eprint/41534