深度学习驱动的金融：期权定价与机器学习实践

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"机器学习在金融领域的应用：深度学习视角下的期权定价探索" 现代科技的飞速发展，特别是在数学分析、计算硬件与软件的进步以及大数据的广泛获取，为金融领域的自动化和智能化提供了可能。本文探讨了人工智能（AI）特别是深度学习如何深刻影响金融行业，以一种普遍的视角回顾过去几十年的研究。在1990年代的工作基础上，作者罗伯特·库尔金和桑吉夫·D·达斯概述了一个适用于金融领域的机器学习框架。该框架特别关注期权定价问题，这是金融衍生品定价的核心组成部分。他们提出了一种全连接的前馈深度学习神经网络，其目标是精确模拟布莱克-斯科尔斯（Black-Scholes，1973年）期权定价模型，这是一种经典的用来评估欧式期权价值的理论工具。深度学习神经网络通过大量历史市场数据进行训练，能够捕捉到复杂的非线性关系，从而实现对期权价格的高效预测。在这个过程中，作者强调了选择合适的超参数至关重要，这些参数决定了模型的精度和性能。他们展示了如何通过优化这些设置，让神经网络能够接近甚至超越专业期权定价交易者的水平，模拟他们在单一股票或指数期权上的交易策略。这项研究不仅验证了深度学习在金融定价中的潜力，还展示了它作为自适应模型的强大能力，能够根据市场动态自我调整并学习新的定价规则。未来，随着技术的进一步发展，这种基于机器学习的期权定价模型有可能成为金融行业中不可或缺的一部分，改变传统定价方法，并为投资管理和风险管理提供更智能的决策支持。此外，这也为其他金融领域的任务，如风险评估、信贷决策和高频交易，开辟了新的可能性。

nature of mathematical calculations in NNs involves matrix calculations in many

dimensions, i.e., using tensors (matrices of dimension greater than 2, usually), and

such calculations are faster when undertaken on graphics processing units (GPUs),

which are now widely used. Indeed, even these are being surpassed by special purpose

computer chips, such as Google’s tensor processing units (or TPUs), so known because

they support tensor calculations. For this reason, Google’s open source deep learning

software is known as TensorFlow.

Third, training machines to replicate and improve on complex human behavior

using NNs is only possible with big data. Learning from experience improves as

more and more examples are considered. We note of course, that too much data

may also be a curse, as the model may be overﬁt in-sample, and hence work poorly

out-of-sample. There is a vast deep learning literature that deals with handling the

overﬁtting problem. However, reasonable sizes of data are needed, and this too has

become much more available today than it ever was before. Ubiquitous data is a

major driver of the success of DL, and a shining example of this success lies in image

recognition, digit recognition, etc. Much of the DL enhancements we have today have

come about because of big, high-quality data, such as that on Image-Net.

Millions

of labeled images are used annually in the ImageNet challenge to ﬁnd the current

best algorithm.

Overall, DL has revolutionized AI, and resulted in its Second New Age. The three

pillars of AI as we have seen are mathematical analysis, computational tractability

using special purpose hardware, and the availability of big data. In the next section

we will consider how Dl may be used to address ﬁnance problems, and examine an

implementation of one such algorithm for option pricing.

2 A Very Brief Overview of Neural Nets

For readers that are unfamiliar with the ﬁeld of deep learning neural nets, we now

provide a brief introduction. Artiﬁcial Neural Networks (ANNs), sometimes referred

https://www.tensorflow.org/.

http://www.image-net.org/.

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