论文标题
深度学习损益
Deep learning Profit & Loss
论文作者
论文摘要
建立投资组合持有的未来利润和损失(P&L)分布除其他资产外,高度非线性和依赖路径的衍生物是一项艰巨的任务。我们提供了一种简单的机械,可以以简单和半自动的方式来考虑越来越多的资产。我们诉诸于最小方的蒙特卡洛算法的变化,其中使用饲料前向神经网络完成了投资组合的持续值的插值。这种方法具有几个吸引人的功能,并非所有这些功能都将在论文中进行充分讨论。神经网络是极其灵活的回归变量。我们不需要担心以下事实:对于多资产的回报,锻炼表面可能是不连接的。我们也不必搜索智能回归器。无论收益的复杂性如何,只有基本过程都要使用。具有许多输出的神经网络可以插值由单个蒙特卡洛模拟产生的投资组合中的每个资产。当不同资产之间的依赖性结构非常强大时,这是一个重要的特征,以说明整个投资组合的损益表的分布,就像一个人在同一基础上写下的有意义的主张一样。
Building the future profit and loss (P&L) distribution of a portfolio holding, among other assets, highly non-linear and path-dependent derivatives is a challenging task. We provide a simple machinery where more and more assets could be accounted for in a simple and semi-automatic fashion. We resort to a variation of the Least Square Monte Carlo algorithm where interpolation of the continuation value of the portfolio is done with a feed forward neural network. This approach has several appealing features not all of them will be fully discussed in the paper. Neural networks are extremely flexible regressors. We do not need to worry about the fact that for multi assets payoff, the exercise surface could be non connected. Neither we have to search for smart regressors. The idea is to use, regardless of the complexity of the payoff, only the underlying processes. Neural networks with many outputs can interpolate every single assets in the portfolio generated by a single Monte Carlo simulation. This is an essential feature to account for the P&L distribution of the whole portfolio when the dependence structure between the different assets is very strong like the case where one has contingent claims written on the same underlying.