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What are some of the things that are currently being researched, or what are the big unanswered questions of quantitative finance that researchers are trying to solve? What are some interesting and extremely important topics being researched with direct massive applications to quantitative finance?

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    $\begingroup$ One topic per answer please. $\endgroup$ – Bob Jansen Oct 19 at 17:40
  • $\begingroup$ No one earns points for community wiki converted questions? $\endgroup$ – develarist Oct 21 at 0:31
  • $\begingroup$ This is correct. $\endgroup$ – Bob Jansen Oct 21 at 5:15
  • $\begingroup$ where can a list of all quant community wikis be found $\endgroup$ – develarist Oct 21 at 12:30
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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 since the introduction of multi curve frameworks.

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  • $\begingroup$ "New products are being developed, models for pricing these products need to be developed (or existing models adapted)": that is of high interest to me. Could you please perhaps edit your answer to give a couple of examples of new products being developed? Are we talking swaptions on SOFR, etc? What in your view would be the main adaptations to existing models related to that? $\endgroup$ – Jan Stuller Oct 21 at 10:34
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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 that most claimed research findings in financial economics are likely false.

Hou, Xue and Zhang (2020, RFS):

Most anomalies fail to hold up to currently acceptable standards for empirical finance. [..] Even for replicated anomalies, their economic magnitudes are much smaller than originally reported. In all, capital markets are more efficient than previously recognized.

There's much research going into developing new econometric tests, including correcting for multiple tests, proposing new test hurdles and higher standards for publication.

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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 (2019) or Horvath, Muguruza & Tomas (2019).

However I am not seeing these methods being implemented in the field yet. In particular, I know that in some places Automatic Adjoint Differentiation (AAD) has been discarded due to the human and temporal resources involved in rewriting pricing libraries to accomodate this technique.

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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 cross-validation techniques, in attempts to generalize better to unseen, test data are:

  • how to estimate financial volatility forecasting models in-sample that can accurately predict unseen test data (out-of-sample) for time horizons longer than 1-day or 5-days ahead.
  • how to estimate optimal portfolio weights in-sample that remain optimal out-of-sample up to the next rebalance date for small (monthly) sample sizes, which is known to increase misestimation error as the available number of historical observations decreases
  • how to forecast asset returns reliably for horizons longer than 1-step ahead, despite them being stationary compared to return volatility, still is an open-ended question, mainly due to the known difficulty (for decades now) in estimating the asset mean

Monte Carlo simulations can indicate how consistent we can expect certain supervised learning algorithms' out-of-sample performance to be, but do not instruct the optimal calibration of hyperparameters for unique, un-simulated, datasets.

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One of the greatest question (which is not only linked to quantitative finance) is, whether $P=NP$. Maymin (2002) found out that markets are efficient if and only if $P=NP$. So one could finally pin that discussion once and for all.

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  • $\begingroup$ Does that relationship work the other way around as well?! $\endgroup$ – StackG Oct 20 at 5:49
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    $\begingroup$ It should, since it is an equivalence statement ("if and only if"). $\endgroup$ – simzoor Oct 20 at 5:51
  • $\begingroup$ Oh yes, exactly right. Very interesting statement then. $\endgroup$ – StackG Oct 20 at 6:16
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    $\begingroup$ Comments on HackerNews: news.ycombinator.com/item?id=24844529, some interesting. $\endgroup$ – Bob Jansen Oct 21 at 12:20
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    $\begingroup$ I don't buy the "if"-part. It seems to assuming away from trading frictions, presence of some noise traders etc. $\endgroup$ – fesman Oct 21 at 13:52

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