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Variance-Optimal Hedging for Processes with Stationary Independent Increments
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Variance-Optimal Hedging for Processes with Stationary Independent Increments
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Journal Article
Variance-Optimal Hedging for Processes with Stationary Independent Increments
2006
Overview
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.
Publisher
Institute of Mathematical Statistics,The Institute of Mathematical Statistics
Subject
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