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Machine Learning algorithms is broadly used in trading strategies and in general when it comes to working with financial time series. The webpage Quantopian is a platform to see some of the possibilities that ML provides in finance.

I was then wondering if ML is also being used in the Q-part of finance when dealing with pricing derivatives, constructing hedging etc. Since this SE doesn't allow opinion based questions I try to be more precise: Are there some research examples out there when ML are being used in Q part of quant finance?

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    $\begingroup$ With all the recent frenzy around ML, I am sure there are papers out there that try to use ML for derivative pricing and hedging tasks (in fact I think I have seen a couple of them on option pricing, using neural networks), which is what the quant "$Q$ world" is about. However, are these lines of research purely academic, or are they being implemented in practice? Personally I am not seeing any ML techniques being used for pricing; maybe on hedging you can find something (e.g. hedging or book optimization for a trading desk). $\endgroup$ – Daneel Olivaw May 6 '18 at 18:37
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    $\begingroup$ Completely agree with Daneel. Since it became a buzzword you'll probably also find "ML" in regression tasks (supervised learning) to estimate the continuation value of callable contingent claim in Monte Carlo. $\endgroup$ – Quantuple May 7 '18 at 8:11
  • $\begingroup$ They would not let you know if they can make money out of their ML strategies anyway :) $\endgroup$ – James May 7 '18 at 18:31
  • $\begingroup$ Not sure you'll find many examples of ML in Q side, due to things like small sample size, and the extra computational complexity against eg closed form methods. $\endgroup$ – amiando Oct 8 '18 at 20:23
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    $\begingroup$ I know from experience that a simple neural network can learn to compute BS implied vol. It’s not faster than typical basic search algos, but it sounds impressive. Good for internal marketing. Beyond that... you can do decent interpolation of complex normally monte-carlo-priced payoffs with 2nd order local polynomials that you can always brand “machine learning”, again purely for internal marketing purposes. This works well for fast indicative pricing. Think “whatever+blockchain” is the one overhyped thing to go for currently though. “Blockchain derivative pricing”. Whatever that may mean. $\endgroup$ – Ivan Oct 9 '18 at 8:35
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There is at least one clear area of application of ML in Q quant finance, it is the LSM algorithm invented by Longstaff, Schwartz and Carriere in the late 1990s for the valuation of callable exotics in the context of Monte-Carlo simulations, and widely adopted for more recent bank-wide risk calculations like CVA.

In order to estimate the continuation value on an exercise date, or a portfolio value on an exposure date, in the context of Monte-Carlo simulations, one would normally need extremely costly nested simulations. The widely adopted LSM algorithm resolves the problem in a particularly elegant manner:

1) Simulate a training set consisting of the simulated state variables of the model on the exercise/exposure date as inputs x, and (discounted) values of future cash-flows in the corresponding scenarios as labels y.

2) Use the simulated training set to train a regression/ANN/deep ANN to estimate f(x) = E[y|x], aka the value on the exercise/exposure date of the remaining cash-flows as a function of the state variables of the model on that date in this scenario.

3) Run Monte-Carlo simulations, applying the trained function f(x) to estimate the future value of the transaction(s) on exercise/exposure dates.

Now I kind of reformulated LSM in modern ML lingo. The original algorithm recommended to find f by linear regression or polynomial regression or more generally by linear regression over basis functions of the state variables.

LSM with basis function regression

We are now acutely aware that deep learning, a powerful generalization of linear regression, produces more accurate results much more effectively (when applied correctly). The correct, efficient estimation of future values in Monte-Carlo simulations is a crucial problem in modern finance, because it is at the heart of most regulated risk calculations: CVA, XVA, CCR, FRTB, PRIIPS, ... Recent advances of ML and DL naturally apply to resolve difficulties with LSM, particularly with many regression variables (high dimensional x)

enter image description here

You will find more on LSM and its application for CVA on my SSRN paper: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2966155 although the paper does not discuss exactly why and how ML/DL helps resolve LSM problems in high dimension, which is an active topic of current research.

I also posted a (more gentle) presentation on similar topics (and with the same limitations) here: https://www.slideshare.net/AntoineSavine/financial-cashflow-scripting-beyond-valuation

Finally, you may want to look at my lecture notes on back-propagation, and particularly the first part, which introduces (very basic) deep learning as an extension of linear regression and shows how DL naturally resolves problems in high dimension: https://github.com/asavine/CompFinance/blob/master/Intro2AADinMachineLearningAndFinance.pdf

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