Semistatic and sparse variance‐optimal hedging
Semistatic and sparse variance‐optimal hedging
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DOI：
10.1111/mafi.12235
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发表时间：
2017-09
影响因子：
1.6
通讯作者：
P. Di Tella;Martin Haubold;Martin Keller-Ressel
中科院分区：
文献类型：
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作者：
P. Di Tella;Martin Haubold;Martin Keller-Ressel
我们考虑的问题对冲未定权益与“半静态”的战略组成的一个动态的立场，在一个资产和静态（购买和持有）的立场，在其他资产。在方差最优准则下，给出了最优策略和套期保值误差的一般表达式，并在赫斯顿模型下，利用傅立叶积分给出了易于处理的公式。我们还考虑了最优选择稀疏半静态套期保值策略的问题，即，一种策略，只使用可用对冲资产的一小部分，并讨论线性回归中变量选择问题的相似之处。开发的方法说明了一个扩展的数值例子，我们计算稀疏的半静态对冲方差互换使用欧式期权作为静态对冲资产。
We consider the problem of hedging a contingent claim with a “semistatic” strategy composed of a dynamic position in one asset and static (buy‐and‐hold) positions in other assets. We give general representations of the optimal strategy and the hedging error under the criterion of variance optimality and provide tractable formulas using Fourier integration in case of the Heston model. We also consider the problem of optimally selecting a sparse semistatic hedging strategy, i.e., a strategy that only uses a small subset of available hedging assets and discuss parallels to the variable‐selection problem in linear regression. The methods developed are illustrated in an extended numerical example where we compute a sparse semistatic hedge for a variance swap using European options as static hedging assets.