A Numerical Method for Hedging Bermudan Options under Model Uncertainty
A Numerical Method for Hedging Bermudan Options under Model Uncertainty
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DOI：
10.1007/s11009-021-09901-6
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发表时间：
2021-11
影响因子：
0.9
通讯作者：
J. Imai
中科院分区：
文献类型：
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作者：
J. Imai
最近，模型不确定性比风险受到更多关注。本研究提出了一种有效的计算框架，以得出在存在模型不确定性的情况下获得百慕大式期权上限和下限的最佳策略。模型不确定性下的最优对冲策略可以表述为极小极大问题的解决方案。我们采用近似动态规划并提出了一种有效解决极小极大问题的算法。本研究将几何布朗运动和指数广义双曲 Lévy 过程作为参考模型。为了考虑模型的不确定性，我们通过 Esscher 或类保留变换考虑一组等效的概率度量。通过数值例子，我们讨论了模型不确定性对跟踪误差大小、对冲投资组合、提前行权的可能性和期权头寸的影响。除了投资者的最优策略之外，该研究还考察了《自然》杂志对等效概率度量的最优选择。我们发现由于模型不确定性的存在而发生的一些值得注意的现象。我们进一步研究不同类型的模型不确定性对期权价值和最优对冲策略的影响。
Model uncertainty has recently been receiving more attention than risk. This study proposes an effective computational framework to derive optimal strategies for obtaining the upper and lower bounds of Bermudan-style options in the presence of model uncertainty. The optimal hedging strategy under model uncertainty can be formulated as a solution of a minimax problem. We employ approximate dynamic programming and propose an algorithm for effectively solving the minimax problem. This study considers a geometric Brownian motion and an exponential generalized hyperbolic Lévy process as reference models. To take model uncertainty into consideration, we consider a set of equivalent probability measures via an Esscher or a class-preserving transform. Using numerical examples, we discuss the effects of model uncertainty on the size of tracking errors, the hedge portfolio, the possibility of early exercise and positions of options. In addition to investors’ optimal strategies, the study examines Nature’s optimal choice for equivalent probability measures. We find several notable phenomena that occur because of the existence of model uncertainty. We further examine the effects of different types of model uncertainty on option values and optimal hedging strategies.