Neural Network Derivatives Pricing for Electricity Commodity Markets

这个研究项目将测试一种用于电力商品衍生品定价的递归神经网络方法。该方法基于动态递归神经网络逼近任意参数泛函的能力。该网络明确估计了金融衍生品的估值。基础资产现货价格过程没有显式复制，但在估计中是隐含的。因此，这种方法克服了许多其他方法中的问题，这些方法侧重于对基本价格过程进行建模。也就是说，明确基于电力等奇异合约基本过程的衍生品定价公式很少以封闭形式出现。几乎所有已知的电力衍生品实时估值方法在计算上都非常昂贵。这种方法将计算成本降低到线下设计，并且应该能够在比通常情况下大大减少的时间内生成在线衍生品估值。该方法在概念上类似于最近的基于变换的方法，这些方法也避免了对基础价格过程的显式估计，但通过在变换域中的替换来隐式地计算衍生价格。然而，在这些变换方法中，所需的解析表达式也不容易出现，从而导致实现它们的计算成本非常高。该方案中提出的设计方法是完全严格的，同时承认计算成本仅略高于典型的离线神经网络训练。在此离线阶段，基于随机回归神经网络最新结果的性能分析方法被用于迭代优化设计，从电价数据序列中提取描述性统计数据，包括与跳跃、价格尖峰和工艺制度切换相关的参数。这些数量被用来对生成衍生资产价格的功能运算符进行参数化。这种方法与已获得闭式衍生产品定价公式的少数和有限情况是一致的。然后，训练递归神经网络以使用由递归神经网络状态反馈的子矢量和(递归神经网络的)外部参数的子矢量组成的输入矢量来生成派生资产价格泛函。动态神经网络方法适合于这种应用，因为对给定时间的期货或远期衍生品合约的理想计算需要在给定日期和衍生品到期日之间以某种自主形式估计数量。训练数据将从实际的电价序列中选择，训练的递归神经网络输出将与实际的衍生品(例如远期)价格进行比较。

9908086OlurotimiThis research project will test a recurrent neural network approach to pricing electricity commodity derivatives. The method is based is based on the ability of dynamic recurrent neural networks to approximate properly parameterized arbitrary functionals. The network explicitly estimates financial derivative valuations. The underlying asset spot price process is not explicitly replicated, but is implicit in the estimation. This approach therefore overcomes the problems in many other approaches that focus on modeling the underlying price process. Namely, derivative pricing equations explicitly based on the underlying process for exotic contracts such as electricity are rarely found in closed form. Virtually all known real time methods for valuing electricity derivatives are extremely computationally expensive. The approach here relegates the computational expense to offline design, and should be able to generate online derivative valuations in dramatically less time than is usually done. The approach is conceptually similar to recent transform based approaches that also avoid explicit estimation of the underlying price process, but compute the derivative prices implicitly through substitutions in the transform domain. However, the desired analytical expressions do not readily emerge in those transform approaches either, leading to very high computational expense in order to implement them. The design approach presented in this proposal is completely rigorous, while admitting a computational cost barely more than typical offline neural network training. Analytical measures of performance based on recent results in stochastic recurrent neural networks are used to iteratively optimize the design in this offline stage.Descriptive statistics are extracted from electricity spot price data series, including parameters related to jumps, price spikes and process regime-switching. These quantities are used to parameterize the functional operator that generates the derivative asset prices. This approach is consistent with those few and limited cases where closed-form derivative pricing formulas have been obtained. The recurrent neural network is then trained to generate the derivative asset price functionals using an input vector that consists of a subvector of the recurrent neural network state feedback, and a subvector of the exogenous (to the recurrent neural network ) parameters. The dynamic neural network approach is suited for this application because the ideal computation of, for example, futures or forward derivative contracts at a given time requires some autonomous form of estimating quantities between the given date and the derivative maturation date.The training data will be selected from actual electricity price series, and the trained recurrent neural network output will be compared with actual derivative (e.g. forward) prices.