6533b828fe1ef96bd12881a0

RESEARCH PRODUCT

A Stieltjes Approach to Static Hedges

Michael SchmutzThomas Zürcher

subject

symbols.namesakeGeneralized functionLebesgue measureDirect methodMathematical analysisBounded variationStochastic gamesymbolsApplied mathematicsRiemann–Stieltjes integralAbsolute continuityLebesgue integrationMathematics

description

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.

yearjournalcountryeditionlanguage
2014-01-01
https://doi.org/10.1007/978-3-319-02069-3_24