A Stieltjes Approach to Static Hedges

Michael Schmutz () and Thomas Zürcher ()
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Michael Schmutz: University of Bern, Mathematical Statistics and Actuarial Science
Thomas Zürcher: University of Jyväskylä, Department of Mathematics and Statistics

A chapter in Inspired by Finance, 2014, pp 519-534 from Springer

Abstract: Abstract 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.

Keywords: Absolute continuity; Bounded variation; Static hedging; Stieltjes integral; 91G20; 26A42; 26A45; 26A46; 26A48; 26A51 (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-02069-3_24

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DOI: 10.1007/978-3-319-02069-3_24

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