The Annals of Applied Probability

Variance-optimal hedging for processes with stationary independent increments

Friedrich Hubalek, Jan Kallsen, and Leszek Krawczyk

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Abstract

We determine the variance-optimal hedge when the logarithm of the underlying price follows a process with stationary independent increments in discrete or continuous time. Although the general solution to this problem is known as backward recursion or backward stochastic differential equation, we show that for this class of processes the optimal endowment and strategy can be expressed more explicitly. The corresponding formulas involve the moment, respectively, cumulant generating function of the underlying process and a Laplace- or Fourier-type representation of the contingent claim. An example illustrates that our formulas are fast and easy to evaluate numerically.

Article information

Source
Ann. Appl. Probab. Volume 16, Number 2 (2006), 853-885.

Dates
First available in Project Euclid: 29 June 2006

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1151592253

Digital Object Identifier
doi:10.1214/105051606000000178

Mathematical Reviews number (MathSciNet)
MR2244435

Zentralblatt MATH identifier
1189.91206

Subjects
Primary: 44A10: Laplace transform 60G51: Processes with independent increments; Lévy processes 91B28

Keywords
Variance-optimal hedging Lévy processes Laplace transform Föllmer–Schweizer decomposition

Citation

Hubalek, Friedrich; Kallsen, Jan; Krawczyk, Leszek. Variance-optimal hedging for processes with stationary independent increments. Ann. Appl. Probab. 16 (2006), no. 2, 853--885. doi:10.1214/105051606000000178. https://projecteuclid.org/euclid.aoap/1151592253


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