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34

Many of them are on my website at emanuelderman.com. Others I probably have anyway. Feel free to email me

26

Hah! There is no such thing as the “rigorous mathematical underpinning” of high frequency trading - because HFT, like all trading, is not primarily a mathematical endeavour. It’s true that many people who work in HFT have a mathematical background, but that’s because the tools of applied math and statistics are useful when analysing the large amounts of ...

19

Rough Volatility Gatheral, Jaisson and Rosenbaum (2018, QF) further popularise a stream of the literature which emphasises the non-smoothness of volatility paths. These models build on a fractional Brownian motion, with Gatheral et al. proposing a Hurst parameter $H<\frac{1}{2}$ and demonstrating the model's ability to match volatility time series. ...

16

I would argue, taking a note from John von Neumman, that quantitative finance lacks rigorous underpinnings. Von Neumann warned in 1953 that many things that look like proofs in economics and finance depended on problems that were yet to be solved in mathematics, and where economists were assuming solutions into existence. As the problems were solved in math,...

15

Partly because it's hard to get a hold of, the Arslan et. al. paper is starting to assume mythical proportions. As said by Dimitri Vulis, the general idea of the paper is set out in (one or two of) Peter Carr's papers. For the benefit of the OP and others I will try to summarize the most salient points of the paper below and also point out the assumptions ...

14

I would say that most ML methods risk overfitting and it depends very much on the asset class. The only area where more sophisticated ML methods such as deep learning appear to make a major difference is in cash equities, where the feature space is very rich (NLP, news and announcements, corporate earnings, other financials) and the data is relatively good, ...

13

If you want to address interesting problems that are interesting for financial mathematics, I do not believe you have the good list. Pricing. For instance, most of explicit formulas for pricing that are not available yet will never be. In this direction, you should have a look at simulation techniques. See for instance Nonlinear Option Pricing. Interesting ...

11

I had read some of them; actually, it does not exist an on-line library that collected them (or, better, it existed here, but it seems the website does not work anymore). I reported here below some of them that you did not find: More Than You Ever Wanted To Know* About Volatility Swaps Model Risk The Volatility Smile And Its implied Tree Enhanced Numerical ...

9

The most pressing topic in the interest rate world is the modelling of the New RFRs (SOFR, SONIA, ESTR etc) as part of the IBOR transition. New products are being developed, models for pricing these products need to be developed (or existing models adapted), and risk models need to be calibrated using limited data. This is probably the biggest development ...

9

As far as empirical asset pricing goes, there occurs to be a replication crisis, similar to other social sciences. Many published results, factors and anomalies cannot be replicated, others don't hold in extended samples or international markets. This questions what we really know about the cross section of returns. Harvey, Liu and Zhu (2016, RFS): We argue ...

9

They are a lot of open problems in market microstructure. To have an idea of the whole landscape, have a look at Market Microstructure in Practice, 2nd Edition, by L and Laruelle. I would split them in From the viewpoint of exchanges Optimal fee schedules to "attract" liquidity (and hence efficient market makers), have a look at Optimal make-take ...

9

Your question comes at this correctly, in my opinion. There is indeed a buyer and a seller behind every option; but the hedging behaviour of the two need not be equivalent... I used to work in an investment bank, and we used to call this (politely) "pin risk", or (less politely) "the gamma hammer". The idea (not perfect, but close enough) ...

8

http://replication.uni-goettingen.de/ (The below text was added by Jan Höffler who founded the wiki.) This site is a replication project for papers, so far mainly in economics but open to any field. It serves as a database of empirical studies, the availability of replication material for them and of replication studies. It can help teaching replication ...

7

What you need is more mutual information rather than Shannon entropy. It is dedicated to capture the influence of one variable on another (you can think about it as a non linear version of Pearson correlations). They are closely related since the mutual information $I$ between two variables $X$ and $Y$ reads: $$I(X;Y) = H(X,Y) - H(X|Y) - H(Y|X)$$ where $H$ ...

7

Rates options Lognormal vs Normal Volatilities and Sensitivities in Practice: this is the best paper on pricing Rates Options in negative rates environment that I have read recently (disclaimer: I don't read many papers, so when I say the "best I read recently" does not necessarily raise the bar very high :). It was published in March 2016, so just ...

6

The application of machine learning to enhance the prediction or forecasting performance of financial models using historical data-driven algorithms (like boosting, support vector machine) has been unable to entirely close the gap between in-sample and out-of-sample performance. Unanswered questions dealing with models fitted using train/test split or other ...

5

TLDR: Massive expansion of credit fuelled by rehypothecation, a general shift to repo, then the scale tips and everyone pays as credit collapses. Quants were there, but I don't think they can be simply blamed for all the ills of the world. There is a general disagreement about what caused what, so some of this is guesswork. I'm marking this a community wiki ...

5

Speech recognition signal processing is complex and possibly similar to the complexity of financial markets. They are similar as per characterictics the non stationarity, noise types and other aspects such us the existence of a spectrum etc conceptual frequency and the grammar to construct and articulate concepts is not evenly and randomly distributed; so ...

5

The field is in flux right now. Since you are at the master's level I think you should focus on more general works in mathematics. If you were my student and we were ignoring specific things such as securities analysis and accounting and focusing on the mathematics, I would recommend you begin with measure theory, real analysis, combinatorics, Bayesian ...

5

It was a Deutsche Bank Working Paper: http://refhub.elsevier.com/S0304-405X(16)00005-2/sbref0001 Unfortunately, it is very hard to find internal research published by banks. I have not seen this one myself, but as far as I know, Peter Carr's published paper has everything that this paper had.

5

Research into leveraging machine learning to speed up models seems to be gaining traction. This can be useful in computationally-expensive problems such as Greeks for products valued through Monte-Carlo, the pricing of valuation adjustments (CVA, FVA, etc.) or optimal collateral posting. See for example Huge & Savine (2020), Itkin (2020), Henry-Labordère ...

4

Recent research A recent article by Frank Zhao is interesting to get started: Natural Language Processing - Part I: Primer. You will find more papers on this repo (too long to copy all here): nlp_papers Applications If you are looking for possible applications of current SoTA research to financial markets, here is a quick list: Equity Predict the ...

4

Ignoring to account for possibly omitted variables Ignoring to account for possibly omitted variables has arguably lead to both of the severe problems below: The fall of the US mortgage market in 2008 as risk on mortgage bond portfolios were grossly underestimated as the strong dependence of their bonds on common variables like the state of the business ...

4

There are tons of quant related blogs out there, some of which contain relatively sophisticated content, others less so. Have a look at the following, which aggregates blogs: MoneyScience Otherwise I could point you to bank/sell-side research. Have a look at the freely available Reuters Messenger (RM), they maintain channels where you can be permissioned ...

4

Start with http://www1.nyse.com/pdfs/closings.pdf which covers all closings through 2011 then use the following information from official exchange sources to get dates up to present day. 2012/2013: http://www1.nyse.com/press/1294398514465.html Weather related closures happened on Monday, Oct. 29, 2012 and Tuesday, Oct. 30, 2012: http://markets.nyx.com/nyse/...

4

I can tell you what I did for my undergraduate thesis (which was a required component on my degree in Mathematics.) I picked a paper on option pricing which gave, as a main result, the closed for solution for the price of an American and Asian Put Option. My contribution was to apply the Fourier Transform to the initial equation in order to simplify the ...

4

Benoit Mandelbrot applied fractals and self-similarity to financial markets and the hurst exponent has its roots in chaos theory. Look at this article from Wilmott magazine. Just a personal note: I have not worked that much with this kind of theory so far but I also have not seen any of my peers being exceptionally sucessfull with these methods.

4

The general idea For equity securities, a simple backtest will typically consist of two steps: Computation of the portfolio return resulting from your portfolio formation rule (or trading strategy) Risk-adjustment of portfolio returns using an asset pricing model Step 2 is simply a regression and computationally very simple in Matlab. What's trickier is ...

4

Journals that have a wider audience tend to have better written papers, such as Journal of Finance, Review of Financial Studies, or Journal of Financial Economics. Editors there try to ensure that papers are accessible to the wider less technical community. In terms of quant authors, my vote goes to Dilip Madan, especially his papers in these journals. I ...

4

I think the answer is driven by asking yourself a few questions : If you are a practitioner at what frequency are you able to trade and want to trade ? (you are limited by this so no need to go to higher frequencies than that in any case) What effect(s) do you want to study ? What is a common frequency used by practitioners or academics for the question ...

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