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A Stieltjes Approach to Static Hedges

In: Inspired by Finance

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  • Michael Schmutz

    (University of Bern, Mathematical Statistics and Actuarial Science)

  • Thomas Zürcher

    (University of Jyväskylä, Department of Mathematics and Statistics)

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.

Suggested Citation

  • Michael Schmutz & Thomas Zürcher, 2014. "A Stieltjes Approach to Static Hedges," Springer Books, in: Yuri Kabanov & Marek Rutkowski & Thaleia Zariphopoulou (ed.), Inspired by Finance, edition 127, pages 519-534, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-02069-3_24
    DOI: 10.1007/978-3-319-02069-3_24
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