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New research, new breakthroughs, and newopportunitiesWhat are the latest innovations by leading quants?
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Contents & introduction
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IntroductionWith many of us in lockdown, our ability to connect with thewider world has been limited to who we can reach online.But if anything proved that the world hasn't stoppedspinning, it would be this brilliant quant community.
In this edition of the QuantMinds eMagazine, we collated thepresentations shown during the QuantMinds Digital Weekby Marcos Lopez de Prado, Alexandre Antonov, SvetlanaBorovkova, and Fabio Mercurio, who have shared their latestinsights into machine learning, neural networks, corona-proof investment strategies, and LIBOR. Antoine Savine andBrian Huge also tell us what happens when machinelearning is combined with AAD!
We hope you are safe and keeping well. We certainly can'twait to welcome you to QuantMinds International later inthe year, but in the meantime, we'd love to hear from you.Give us a shoutout on Twitter and LinkedIn - let's keep intouch.
The QuantMinds Team
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ContentDifferential machinelearningAntoine Savine & Brian Huge,
Danske Bank
Machine learning assetallocationWebinar presented by Marcos
Lopez de Prado, True Positive
Technologies
Neural networks withasymptotics controlWebinar presented by Alexandre
Antonov, Danske Bank
Corona-immunise yourportfolio: from globalmacro trends to corona-proof quant investingWebinar presented by Svetlana
Borovkova, Vrije Universiteit
Amsterdam
Looking forward tobackward-looking rates:completing thegeneralised forwardmarket modelWebinar presented by Fabio
Mercurio, Bloomberg L.P.
Online training for quantfinance professionalsFrom our learning partner IFF
Differential machine learningAntoine Savine and Brian Huge, Danske Bank
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AAD revolutionized both ML and finance. In ML, where itis called backpropagation, it allowed training deep neuralnetworks (NN) in reasonable time and the subsequent successof e.g. computer vision or natural language processing. Infinance, AAD computes vast numbers of differentialsensitivities, with analytic accuracy and miraculous speed,giving us instantaneous model calibration and realtime riskreports of complex trading books.
Recall how we produce Monte-Carlorisk reports. We first computepathwise differentials, thesensitivities of (adequatelysmoothed) payoffs (sum ofcashflows) wrt market variables,path by path across simulations, seethis tutorial for a refresh. Then, weaverage sensitivities across Monte-Carlo paths to produce the riskreport, collapsing a wealth ofinformation into aggregatedmetrics. For example, consider adelta-hedged European call. Therisk report only shows a delta of
zero, from that point of view it mightas well be an empty book. But beforecollapsing into a risk report,pathwise differentials measured thenonlinear impact of the underlyingprice on the final outcome in a largenumber of scenarios. This is a vastamount of information, from whichwe can e.g. extract the principal riskfactors over the transaction lifetime,identify static hedges and measuretheir effectiveness, or learn pricingand risk function of market stateson future dates.
AAD made differentialsmassively available infinance, opening a world ofpossibilities, of which weonly scratched the surface.Realtime risk reports areonly the beginning.
In Danske Bank, where AAD wasfully implemented in productionearly, the pathwise sensitivities ofcomplex trading books are readilyavailable for research anddevelopment of improved riskmanagement strategies. Superflyanalytics, Danske Bank’squantitative research department,initiated a major project to train anew breed of ML models onpathwise differentials to learneffective pricing and risk functions.The trained models are capable ofcomputing value and risks functionsof the market state with nearanalytic speed, effectively resolvingcomputation load of scenario basedrisk reports, backtesting of hedgestrategies or regulations like XVA,CCR, FRTB or SIMM-MVA.
We published a detailed descriptionin a working paper, along withnumerical results and a vastamount of additional material(mathematical proofs, practicalimplementation details andextensions to other ML models thanNN) in online appendices. We alsoposted a simple TensorFlowimplementation on the companionGitHub repo. You can run it onGoogle Colab. Don’t forget toenable GPU support in the Runtimemenu.
As expected, we found thatmodels trained ondifferentials with adequatealgorithms vastlyoutperform existingmachine learning and deeplearning (DL) methodologies.
As a simple example, consider 15stocks in a correlated Bacheliermodel. We want to learn the priceof a basket option as a function ofthe 15 stocks. Of course, the correctsolution is known in closed form sowe can easily measureperformance. We trained astandard DL model on m simulatedexamples with initial state X (avector in dimension 15) along withpayoff Y (a real number), a laLongstaff-Schwartz. We also traineda differential DL model on a trainingset augmented with pathwisedifferentials Z=dY/dX, and testedperformance against the correctformula on an independent dataset.
Differential training learns withremarkable accuracy on smalldatasets, making it applicable inrealistic situations. The results carryover to transactions and simulationmodels or arbitrary complexity. Infact, the improvement fromdifferential ML considerablyincreases with complexity. Forexample, we simulated thecashflows of a medium sizedDanske Bank netting set, includingsingle and cross currency swapsand swaptions in 10 differentcurrencies in Danske Bank’sproprietary XVA model, where
interest rates are simulated with afour-factor, sixteen-statemultifactor Cheyette model percurrency, and comparedperformance of a standard DLmodel trained on 64k paths with adifferential model trained on 8kpaths. Evidently, we don’t have aclosed form to compare with,instead, we ran nested simulationsovernight as a reference. The chartbelow shows performance on anindependent test set, with correct(nested) values on the horizontalaxis and predictions of the trainedML models on the vertical axis.
The trained neural netapproximates the price in its outputlayer by feedforward inference fromthe state variables in the input layer.The gradient of the price wrt thestate is effectively computed bybackpropagation. By makingbackprop part of the network, we geta twin network capable of predictingprices together with Greeks.
We see that differential ML achieves high quality approximation on smalldatasets, unthinkable with standard ML even on much bigger training sets.A correct articulation of AAD with ML gives us unreasonably effective pricingapproximation in realistic time.
Besides, the core idea is very simple, and its implementation isstraightforward, as seen on the TensorFlow notebook.
All that remains is train the twin network to predict correct prices andGreeks by minimisation of a cost function combining prediction errorson values and differentials, as compared with differential labels, a.k.a. thepathwise differentials computed with AAD:
Differential training imposes apenalty on incorrect Greeks in thesame way that traditionalregularisation like Tikhonov favorssmall weights. Contrarily toconventional regularisation,differential ML effectively mitigatesoverfitting without introducing a bias.To see this, consider training ondifferentials alone. We prove in themathematical appendix that thetrained model converges to anapproximation with all the correctdifferentials, i.e. the correct pricing
function modulo an additiveconstant. Hence, there is no bias-variance tradeoff or necessity totweak hyperparameters by crossvalidation. It just works.
Differential machine learning ismore similar to data augmentation,which in turn may be seen as abetter form of regularisation. Dataaugmentation is consistentlyapplied e.g. in computer vision withdocumented success. The idea is toproduce multiple labeled images
from a single one, e.g. by cropping,zooming, rotation or recoloring. Inaddition to extending the trainingset for negligible cost, dataaugmentation teaches the MLmodel important invariances.Similarly, derivatives labels, not onlyincrease the amount of informationin the training set for very small cost(as long as they are computed withAAD), but also teach ML models theshape of pricing functions.
Working paper: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3591734
Github repo: https://github.com/differential-machine-learning
About the authors
Antoine Savine and Brian Huge are affiliated with Superfly Analytics at Danske Bank, winner of the RiskMinds 2019award Excellence in Risk Management and Modelling.
Prior to joining Danske Bank in 2013, Antoine held multiple leadershippositions in quantitative finance, including Head of Research at BNP-Paribas. He also teaches volatility and computational finance atCopenhagen University. He is best known for his work on volatility andrates, and he was influential in the wide adoption of cashflow scripting infinance. At Danske Bank, Antoine wrote the book on AAD with Wiley and wasa key contributor to the bank’s XVA system, winner of the In-House Systemof the Year 2015 Risk award.
Brian works in Danske Bank quantitative research since 2001 and producedvery noticeable contributions in quantitative finance with Jesper Andreasen,including the iconic ZABR: expansion for the masses, or the LVI volatilityinterpolation method coupled with the Random Grid algorithm, winnerof the Quant of the Year 2012 Risk award. All those algorithms areimplemented in Superfly, Danske Bank’s proprietary risk managementplatform, and used every day for the management of the bank’s tradingbooks.
Antoine and Brian both hold PhDs in mathematics from CopenhagenUniversity. They are regular speakers on QuantMinds and RiskMinds events.
Machine learning assetallocationWebinar presented by Marcos Lopez dePrado, CIO, True Positive Technologies
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Marcos Lopez de Prado, CIO, TruePositive Technologies
Convex optimisation solutions tend to be unstable, to thepoint of entirely offsetting the benefits of optimisation. Forexample, in the context of financial applications, it is knownthat portfolios optimised in sample often underperform thenaïve (equal weights) allocation out of sample. This instabilitycan be traced back to two sources:
1. noise in the input variables; and2. signal structure that magnifies the estimation errors in
the input variables.
There is abundant literature discussing noise inducedinstability. In contrast, signal induced instability is oftenignored or misunderstood. We introduce a new optimisationmethod that is robust to signal induced instability.
Working paper: https://ssrn.com/abstract=3469964
Neural networks with asymptotics controlWebinar presented by Alexandre Antonov, Chief Analyst, Danske Bank
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Artificial neural networks(ANNs) have recently beenproposed as accurate andfast approximators invarious derivatives pricingapplications. ANNs typicallyexcel in fitting functions theyapproximate at the inputparameters they are trainedon, and often are quite goodin interpolating betweenthem. However, for standardANNs, their extrapolationbehaviour – an importantaspect for financialapplications – cannot becontrolled due to complexfunctional forms typicallyinvolved. We overcome thissignificant limitation anddevelop a new type of neuralnetworks that incorporatelarge-value asymptotics,
when known, allowingexplicit control overextrapolation.
This new type ofasymptotics-controlledANNs is based on two noveltechnical constructs, a multi-dimensional splineinterpolator with prescribedasymptotic behaviour, and acustom ANN layer thatguarantees zero asymptoticsin chosen directions.Asymptotics control brings anumber of importantbenefits to ANN applicationsin finance such as well-controlled behaviour understress scenarios, gracefulhandling of regime switching,and improvedinterpretability.
Alexandre Antonov, Chief Analyst,Danske Bank
Presentation: https://bit.ly/2AfVrO4
Corona-immunise your portfolio: from globalmacro trends to corona-proof quant investingWebinar presented by Svetlana Borovkova, Associate Professor Of Quantitative Finance, VrijeUniversiteit Amsterdam
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Svetlana Borovkova, Associate Professor Of QuantitativeFinance, Vrije Universiteit Amsterdam
One can only speculate how the world will look like after thecoronavirus epidemic. But some of the macroeconomic andconsumer trends we can observe already now.
Using alternative data such as sentiment and searchbehaviour, I will outline several emerging trends andtranslate them into scenarios, which can be used to assessstock portfolios in terms of their resistance in the post-corona world. I will address factors such as quality andsustainability, but also other, new post-corona factors willplay important role in immunising your stock portfolioagainst corona effects.
Finally, I will touch upon risk and modelling challenges ofrecently observed negative oil prices.
Presentation: https://bit.ly/2AcKgpl
Lookingforward tobackward-looking rates:completing thegeneralisedforward marketmodelWebinar presented by FabioMercurio, Global Head ofQuant Analytics, BloombergL.P.
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In this talk, we show how thegeneralised forward marketmodel (FMM) introduced byLyashenko and Mercurio(2019) can be extended tomake it a complete term-structure model describingthe evolution of all points ona yield curve, as well as thatof the bank account. Theability to model the bankaccount, in addition to theforward curve, is going to beof crucial importance onceLibor rates are replaced with
setting-in-arrears rates inderivative and cashcontracts, where fixings aredefined in terms of therealised bank accountvalues.
To achieve our goal, we“embed” the FMM into aMarkovian HJM model withseparable volatility structureby aligning the HJM and FMMdynamics of the forwardterm rates modelled by theFMM. This FMM-aligned HJM
Fabio Mercurio, Global Head of QuantAnalytics, Bloomberg L. P.
Presentation: https://bit.ly/2zBY0Kd
model is effectively a hybridbetween an instantaneousforward-rate model and aLMM, and shares theadvantages of bothapproaches, with the caveatthat the number of variablesto simulate could be toohigh.
A more efficient approach isthen derived by expressingthe zero-coupon bonds andthe bank account asfunctions of the modelledforward term rates and theirvolatilities. In this FMM-HJMconstruct, FMM acts as a“coarse” model capturing a“macro” structure of themarket such as thecovariance structure of theset of modelled rates, while
the FMM-aligned HJM servesas a finer modellingenvironment used to fill thegaps left by the coarserFMM.
The problem of recoveringthe whole yield curveevolution from the modelledset of Libor rates has beenextensively discussed in theLMM literature, and is oftenreferred to as Libor-rateinterpolation, or front- andback-stub interpolations.Contrary to existingmethods, the approach wepropose is not onlyarbitrage-free byconstruction, but it alsoallows for the generation ofbank account values.
Online training for quant finance professionalsFrom our learning partner IFF
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With COVID-19 affecting the way the vast majority of us are working, this is a great time tobe consolidating and building knowledge. Online training is the most convenient way to addto your skills or get new qualifications as a team and be ready for when life returns to the newnormal.
We spoke to Jeff Hearn, Managing Director at IFF, our official training partner.
“We have seen a big rise in interest for our portfolio of courses,developed in partnership with Middlesex University since lockdown.All the courses are delivered 100% online and offer considerableaccess to expert trainers. IFF launched its first digital training course10 years ago and we have been adapting and improving them eversince. Our distance learning courses have regular start dates and,after completing the modules, you can work on an assignment toqualify for a postgraduate certificate.”
Find out more aboutsome of the courses,created for quantfinance professionals. Amodule is releasedevery two weeks,usually for 14-16weeks.
Derivatives &Financial Products
Fintech & AI
Loan Documentation
Trade FinanceMany of IFF’s clients adapt these programmes or ask for bespoke content. IFF consultants can work with you andthe trainers to develop a tailored solution for you, using webinars, videos, case studies and our online learningplatform. They excel at finding the perfect package for you, combining different delivery methods with bespokecontent that incorporates the actual issues your team is facing.
Contact Jeff Hearn – [email protected]
Contact Jeff Hearn – [email protected]
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Do you want to be involved in a futureQuantMinds eMagazine or event?Get in touch for speaking opportunities:[email protected] in touch for sponsorship opportunities:[email protected]@informa.com
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