Variance-Optimal Hedging for Processes with Stationary Independent Increments
Variance-Optimal Hedging for Processes with Stationary Independent Increments
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DOI：
10.1214/105051606000000178
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发表时间：
2006-05
影响因子：
1.8
通讯作者：
F. Hubalek;J. Kallsen;Leszek Krawczyk
中科院分区：
文献类型：
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作者：
F. Hubalek;J. Kallsen;Leszek Krawczyk
当标的资产价格的对数在离散时间或连续时间内服从平稳独立增量过程时，我们确定了方差最优套期保值。虽然这个问题的一般解决方案被称为向后递归或向后随机微分方程，我们表明，这类过程的最佳禀赋和战略可以更明确地表示。相应的计算公式包括弯矩和弯矩。潜在过程的累积生成函数和或有索赔的拉普拉斯型或傅立叶型表示。一个例子表明，我们的公式是快速和容易的数值评估。
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.