Variance-Optimal Hedging for Processes with Stationary Independent Increments

By Friedrich Hubalek, Jan Kallsen, Leszek Krawczyk. 2006

126 citations recorded by the source corpus.

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 resp. 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.

View Paper: https://www.semanticscholar.org/paper/f18d9bf49087bfe2f140c4b0302655af979e41a5

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Citations in the corpus

Asymptotic analysis of hedging errors in models with jumps (2009, result): “Another approach is to compute the variance-optimal quadratic hedge ratio directly under the historical measure [ 17 ].”
Pricing and Hedging in Exponential Lévy Models: Review of Recent Results (2011, methodology): “[29] exploit these results to derive explicit formulas for the hedging strategy in the case of Lévy processes.”
Affine Diffusion Processes: Theory and Applications (2009, background): “More examples of payoff functions with integral representation, including the above, can be found in [22].”
FOURIER TRANSFORM METHODS FOR REGIME-SWITCHING JUMP-DIFFUSIONS AND THE PRICING OF FORWARD STARTING OPTIONS (2011, background): “ave been successfully applied to a variety of pricing problems in the last years. Among the various contributions to this theory, see Bakshi and Madan (2000), Raible (2000), Lewis (2002), Lee (2004), Hubalek et al. (2006), Biagini et al. (2008), and more recently Cherubini et al. (2009), Dufresne et”
On the Structure of General Mean-Variance Hedging Strategies (2007, unknown): “More recent publications in this context include [2, 3, 4, 7, 8, 9, 10, 11, 17, 23, 24, 25, 26, 32, 33, 34, 35, 36, 46].”
Hedging with options in models with jumps (2007, unknown): “framework”
MEAN–VARIANCE HEDGING AND OPTIMAL INVESTMENT IN HESTON'S MODEL WITH CORRELATION (2008, unknown): “…one obtains Vt = EQ (∫ β+i∞ β−i∞ π (z)ez ln ST dz ∣∣∣∣Ft ) = ∫ β+i∞ β−i∞ π (z)ev0(t,z)+v1(t,z)Y 2 t +z ln St dz,(4.2) where β ∈ R is a suitably chosen constant and π (z) are the Fourier coefficients of the contingent claim (cf. Černý 2007; Hubalek et al. 2006), H = ∫ β+i∞ β−i∞ π (z)ez ln ST dz.”
Analysis of Fourier Transform Valuation Formulas and Applications (2008, background): “The article of Borovkov and Novikov (2002) deals with the application of Fourier transform valuation formulas for the pricing of some exotic options, while Hubalek et al. (2006) use similar techniques for hedging purposes.”