We survey the active interface of statistical learning methods and quantitative finance models. Our focus is on the use of statistical surrogates, also known as functional approximators, for learning input–output relationships relevant for financial tasks. Given the disparate terminology used among statisticians and financial mathematicians, we begin by reviewing the main ingredients of surrogate construction and the motivating financial tasks. We then summarize the major surrogate types, including (deep) neural networks, Gaussian processes, gradient boosting machines, smoothing splines, and Chebyshev polynomials. The second half of the article dives deeper into the major applications of statistical learning in finance, covering ( a) parametric option pricing, ( b) learning the implied/local volatility surface, ( c) learning option sensitivities, ( d) American option pricing, and ( e) model calibration. We also briefly detail statistical learning for stochastic control and reinforcement learning, two areas of research exploding in popularity in quantitative finance.

中文翻译：

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定量金融统计机器学习


我们调查了统计学习方法和定量金融模型的活跃界面。我们的重点是使用统计代理（也称为函数逼近器）来学习与财务任务相关的输入输出关系。鉴于统计学家和金融数学家使用不同的术语，我们首先回顾一下替代构建的主要成分和激励金融任务。然后，我们总结了主要的代理类型，包括（深度）神经网络、高斯过程、梯度增强机、平滑样条和切比雪夫多项式。本文的后半部分深入探讨了统计学习在金融领域的主要应用，涵盖 (a) 参数期权定价，(b) 学习隐含/局部波动率表面，(c) 学习期权敏感性，(d) 美式期权定价，和（e）模型校准。我们还简要详细介绍了随机控制和强化学习的统计学习，这两个研究领域在量化金融中迅速流行。