Abstract

In this article, we present the American option pricing procedure based on the binomial tree from an imprecise statistical aspect. Nonparametric Predictive Inference (NPI) is implemented to infer imprecise probabilities of underlying asset movements, reflecting uncertainty while learning from data, which is superior to the constant risk-neutral probability. In a recent article, we applied the NPI method to the European option pricing procedure that gives good results when the investor has non-perfect information. We now investigate the NPI method for American option pricing, of which imprecise probabilities are considered and updated for every one-time-step path. Different from the classic models, this method is shown that it may be optimal to early exercise an American non-dividend call option because our method considers all information that occurs in the future steps. We also study the performance of the NPI pricing method for American options via simulations in two different scenarios compared to the Cox, Ross and Rubinstein binomial tree model (CRR), first where the CRR assumptions are right, and second where the CRR model uses wrong assumptions. Through the performance study, we conclude that the investor using the NPI method tends to achieve good results in the second scenario.

摘要

在本文中，我们从不精确的统计角度介绍了基于二叉树的美式期权定价程序。非参数预测推理 (NPI) 用于推断基础资产移动的不精确概率，反映在从数据中学习时的不确定性，优于恒定风险中性概率。在最近的一篇文章中，我们将 NPI 方法应用于欧式期权定价程序，当投资者拥有非完美信息时，该程序会给出良好的结果。我们现在研究美式期权定价的 NPI 方法，其中不精确的概率被考虑和更新为每个一次性路径。与经典款不同，该方法表明，提前行使美式非股息看涨期权可能是最佳选择，因为我们的方法考虑了未来步骤中发生的所有信息。与 Cox、Ross 和 Rubinstein 二叉树模型 (CRR) 相比，我们还通过在两种不同场景中的模拟来研究美式期权的 NPI 定价方法的性能，首先是 CRR 假设是正确的，其次是 CRR 模型使用错误的假设。通过绩效研究，我们得出结论，使用 NPI 方法的投资者在第二种情况下往往会取得良好的结果。其次，CRR 模型使用了错误的假设。通过绩效研究，我们得出结论，使用 NPI 方法的投资者在第二种情况下往往会取得良好的结果。其次，CRR 模型使用了错误的假设。通过绩效研究，我们得出结论，使用 NPI 方法的投资者在第二种情况下往往会取得良好的结果。