论文标题
使用回归树/随机森林的定价百慕大选项
Pricing Bermudan options using regression trees/random forests
论文作者
论文摘要
美国期权的价值是该期权折现现金流的最大值。在每个时间步骤中，都需要将即时的锻炼价值与持续价值进行比较，并决定在严格的锻炼价值大于延续价值的情况下立即进行锻炼。我们可以将此问题提出为动态编程方程，其中主要难度来自代表每个时间步骤延续值的条件期望的计算。在（Longstaff和Schwartz，2001）中，使用有限维矢量空间（通常是多项式基础）的回归估算了这些条件期望。在本文中，我们遵循相同的算法；仅使用回归树或随机森林估算条件期望。我们讨论当标准最小二乘回归被回归树代替时，LS算法的收敛性。最后，我们通过回归树和随机森林暴露了一些数值结果。随机森林算法在高维度中可获得出色的结果。
The value of an American option is the maximized value of the discounted cash flows from the option. At each time step, one needs to compare the immediate exercise value with the continuation value and decide to exercise as soon as the exercise value is strictly greater than the continuation value. We can formulate this problem as a dynamic programming equation, where the main difficulty comes from the computation of the conditional expectations representing the continuation values at each time step. In (Longstaff and Schwartz, 2001), these conditional expectations were estimated using regressions on a finite-dimensional vector space (typically a polynomial basis). In this paper, we follow the same algorithm; only the conditional expectations are estimated using Regression trees or Random forests. We discuss the convergence of the LS algorithm when the standard least squares regression is replaced with regression trees. Finally, we expose some numerical results with regression trees and random forests. The random forest algorithm gives excellent results in high dimensions.
