I was struck by the fact that most techniques and ideas apply also to problems in quantitative finance.
- Linear regression: used for example in the Longstaff-Schwartz approach to price Bermudan options with Monte-Carlo. Interestingly the teacher insists on feature normalization, something we can forget easily, especially with the polynomial features.
- Gradient descent: one of the most basic minimizer and we use minimizers all the time for model calibration.
- Regularization: in finance, this is sometimes used to smooth out the volatility surface, or can be useful to add stability in calibration. The lessons are very practical, they explain well how to find the right value of the regularization parameter.
- Neural networks: calibrating a model is very much like training a neural network. The backpropagation is the same thing as the adjoint differentiation. It's very interesting to see that it is a key feature for Neural networks, otherwise training would be much too slow and Neural networks would not be practical. Once the network is trained, it is evaluated relatively quickly forward. It's basically the same thing as calibration and then pricing.
- Support vector machines: A gaussian kernel is often used to represent the frontier. We find the same idea in the particle Monte-Carlo method.
- Principal component analysis: can be applied to the covariance matrix square root in Monte-Carlo simulations, or to "compress" large baskets, as well as for portfolio risk.
While it sounds like a straightforward remark, I have found that people (including myself) tend to do the same mistakes in finance. We might use some quadrature, find out it does not perform that well in some cases, replace it with another one that behaves a bit better, without investigating the real issue: why does the first quadrature break? is the new quadrature really fixing the issue?