英文标题：
《Discounted optimal stopping of a Brownian bridge, with application to
American options under pinning》
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作者：
Bernardo D\'Auria and Eduardo Garc\\\'ia-Portugu\\\'es and Abel Guada
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最新提交年份：
2020
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英文摘要：
Mathematically, the execution of an American-style financial derivative is commonly reduced to solving an optimal stopping problem. Breaking the general assumption that the knowledge of the holder is restricted to the price history of the underlying asset, we allow for the disclosure of future information about the terminal price of the asset by modeling it as a Brownian bridge. This model may be used under special market conditions, in particular we focus on what in the literature is known as the \"pinning effect\", that is, when the price of the asset approaches the strike price of a highly-traded option close to its expiration date. Our main mathematical contribution is in characterizing the solution to the optimal stopping problem when the gain function includes the discount factor. We show how to numerically compute the solution and we analyze the effect of the volatility estimation on the strategy by computing the confidence curves around the optimal stopping boundary. Finally, we compare our method with the optimal exercise time based on a geometric Brownian motion by using real data exhibiting pinning.
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中文摘要：
从数学上讲，美式金融衍生品的执行通常被简化为解决最优停止问题。打破了持有人的知识仅限于标的资产的价格历史的一般假设，我们允许通过将资产的最终价格建模为布朗桥来披露有关资产的未来信息。该模型可在特殊的市场条件下使用，特别是我们关注文献中所称的“钉扎效应”，即当资产价格接近高度交易期权的执行价格时，接近其到期日。我们的主要数学贡献在于，当增益函数包含折扣因子时，描述最优停止问题的解。我们展示了如何数值计算解，并通过计算最优停止边界附近的置信曲线来分析波动率估计对策略的影响。最后，我们使用显示钉扎的真实数据，将我们的方法与基于几何布朗运动的最佳运动时间进行了比较。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Computational Finance 计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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