非高斯GARCH模型的二次套期保值方案
Quadratic hedging schemes for non-Gaussian GARCH models
摘要：
我们提出了不同的方案时，资产收益率建模使用一般类的GARCH模型的期权套期保值。更具体地说，我们实现了本地风险最小化和最小方差套期保值近似的基础上扩展Girsanov原则，推广段（1995年）的三角洲套期保值。由于最小鞅测度在这种情况下不能产生概率测度，我们构造了关于定价核的局部风险最小化套期保值策略。这些方法的背景下，非高斯驱动的模型进行了研究。此外，我们分析了这些方法的非高斯Gestival扩散极限过程，并将它们链接到相应的离散时间对应。一个详细的数值分析的基础上，标准普尔500欧洲看涨期权提供评估所提出的计划的实证性能。我们还测试了对冲策略的灵敏度相对于风险中性测度重新计算我们的一些结果与指数仿射定价内核。
英文摘要：
We propose different schemes for option hedging when asset returns are modeled using a general class of GARCH models. More specifically, we implement local risk minimization and a minimum variance hedge approximation based on an extended Girsanov principle that generalizes Duan's (1995) delta hedge. Since the minimal martingale measure fails to produce a probability measure in this setting, we construct local risk minimization hedging strategies with respect to a pricing kernel. These approaches are investigated in the context of non-Gaussian driven models. Furthermore, we analyze these methods for non-Gaussian GARCH diffusion limit processes and link them to the corresponding discrete time counterparts. A detailed numerical analysis based on S&P 500 European Call options is provided to assess the empirical performance of the proposed schemes. We also test the sensitivity of the hedging strategies with respect to the risk neutral measure used by recomputing some of our results with an exponential affine pricing kernel.
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