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Day 3 opened with Emanuel Derman presenting “The Past and Future of Quantitative Finance”:

In “Derivatives without Diffusion”, Derman shows how Spinoza defined emotions as derivatives of the underlying primitive affects of Desire, Pleasure and Pain. The composition of schadenfraude (literally harm-joy) is an example of how these affects can be combined; but most of its definitions are static, with only vacillation involving volatility. The answer to why Spinoza had no anxiety in his system (Vacillation between Hope and Fear? Not a Passion? No Anxiety in the 17th Century?) was left as exercise to the reader/audience. My take is that increased social mobility has increased both the Hope of progression and the Fear of regression.

In “Diffusion without Derivatives”, physicists are shown to have understood diffusion in the 19th and early 20th centuries but, with the exception of Bachelier, they never extended this understanding to derivatives of the underlying particles.

In “The Idea of Replication”, this strategy opens up new avenues for valuation and risk management:

How to avoid risk?

(i) Dilution: Combine security with a riskless bond

(ii) Diversification: Combine security with many uncorrelated securities

(iii) Hedging: Combine security with a correlated security

Then, in the style of Feynman, modern finance is synthesized in one sentence:

“If you can hedge away all correlated risk

And you can then diversify over all uncorrelated risk

Then you should expect only to earn the riskless rate.”

This leads to CAPM: equal (unavoidable) risk expects equal return; but CAPM is not realistic.

There is a counterfactual illusion of probability:

It’s worth reading Peters and Gell-Mann ( https://arxiv.org/abs/1405.0585 ) and Taleb ( https://medium.com/incerto/the-logic-of-risk-taking-107bf41029d3 ) on this concept (ensemble x time, sequence matters). This is probably one of the most important topics to study in finance.

Even though options were priced and hedged in the 60s, only in the 70s every piece of the puzzle (diffusion+volatility+hedging+replication) was put together in the BSM framework.

A stock is very correlated with an option written on it; this connection is much stronger (and more true) than the statistical connection between two stocks, or the stock and the market; but volatility itself might be random, leading to a true derivative definition only at expiration.

Because hedged option traders were indifferent to the return of the stock, what they were forecasting and trading was the future volatility of the stock. But implied volatilities change every day. They are not a consequence of the past. They are raised and twisted and bent by customer demand and risk perception; but on trying to get information from them, the market starts calibrating models: fitting parameters to the traded prices; Derman highlights the publication of “Standard Deviations of Stock Price Ratios Implied in Option Prices”, by Latané and Rendleman (The Journal of Finance, May 1976) as critical in the origin of the rise of calibration. And now we get volatility as an asset class, with options as a means to an end.

Quantitative finance started to develop by attracting physicists (like Derman himself), but while in physics the future is always a consequence from the present, in finance you calibrate the future using present prices, and then come back to the present to predict other present prices (“And the end of all our exploring / Will be to arrive where we started”).

As markets and models grow more complex, calibration still continue to update unstable parameters at every iteration, as we trade volatility of volatility without a theory (or even a consensus model). As Rebonato pointed out during the event, when Pat Hagan was asked about the fit of SABR to the markets, he said: “In the beginning, it was not perfect, but after everyone started using it then it fit perfectly”. That is perhaps the great difference between Physics and Finance: electrons didn’t change their behaviour when our models of the atom changed.

As for the present and future, Derman pointed out the shift from:

(i) sell-side to buy-side

(ii) q quants (structural/derivative) to p quants (econometric/statistical)

While pointing out the risks of wrong models and lack of reproducibility in social sciences.

Market microstructure, enabled by the electronification of the markets and the availability of high-frequency data, is among the fields where the modeling has shifted back to the underlying assets and statistical approaches.

And now curiously a stock is not a single entity anymore; if today each food item is seen by some as a basket of nutrients, financial assets like stocks are now traded according to (statistical) factors and even who holds them is now used as a predictor of returns. Again, the Earth did not change its orbit as we went from epicycles to Kepler to Newton, but today everyone is invited to add their money to levers that will push the market into a new path that will not resemble the past. As the final slide points out, there are no reliable theorems in finance; it’s not math, it’s the world.

Quire a long commentary, but Derman’s ideas about the limitations of models are always worth considering, especially as a new generation arrives with powerful tools and a new hope for building a system of the world.

The plenary section was treated to another kind of model reevaluation with the anecdotes of freakyclown, co-founder of Redacted Firm and a social engineer / ethical hacker. Those of who have read Bruce Schneier know how he shifted his point of view about security from the technological to the holistic, paying special attention to the human element. In this presentation, freakyclown focused on the physical/human element of security, in an eye-opening collection of incidents that elicited laughs but hopefully reflections. About two years ago I read “A Burglar’s Guide to The City”, by Geoff Manaugh, and this presentation also should make one incorporate an attacker’s point of view in his/her daily life.

Damiano Brigo and Peter Carr also presented on Day 3, and Alexander Lipton pointed out the way for new financial services companies to disrupt the existing business of banks (e.g. WeChat).

Saeed Amen (Cuemacro) chaired Stream A, where a presentation on machine learning applied to FX trading by Patrik Karlsson had interesting comments on how to account for your actions and restrictions by Santander’s Francesca Fiorilli. The following presentation (“Implied volatility with bivariate Checyshev interpolation” by Kathrin Glau) had interesting results (fast results within a chosen precision) and also benefited from comments (Peter Jaeckel was present). Saeed and his colleague Shih-Hau Tan discussed FX trading (news, TCA and Python libraries – check them out here:  https://github.com/cuemacro/finmarketpy and check Saeed’s comments on the event here: http://www.cuemacro.com/2018/05/21/quantminds-lisbon-2018/ ).

An appropriate closure came with “Learning Rough Volatility” by Aitor Gonzalez. He finds that the most convincing argument for rough volatility is its forecasting power (based on the past realisation), and that combining the historical data with the market’s variance swap quotes we can infer the market premium of risk. Adding and exponential term allows for mean reversion, and an quite good parametrization (5 factors) of the whole surface with an efficient simulation leading to fast calibration.

Overall, rough volatility seems like a promising way to find the time future contained in time past.

And that concludes my analysis of the event (I was not there for the seminars).

As always, any errors on the interpretation of the presentations/papers are the responsibility of Marcos.

What would you be reading if you were interested in volatility modeling?

In the 90s one would read the papers from Derman and Dupire.

In the 00s books like Gatheral’s “The Volatility Surface” and Rebonato’s “Volatility and Correlation: The Perfect Hedger and the Fox” were mandatory.

In this decade one must know the Bergomi-Guyon expansion ( https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1967470 ) and read Bergomi’s “Stochastic Volatility Modeling” for volatility surface modeling, and the recent developments in rough volatility ( the literature is collected here https://sites.google.com/site/roughvol/home ).

All of the researchers above were here in Lisbon, and the opportunity of being able to discuss and learn from them is what makes this event special.

And one talk in special, Jim Gatheral’s “Diamonds: A quant’s best friend”, was a great way to know what’s happening in the field.

With 5 tracks, it’s hard to attend every interesting talk, and most of the day I was looking at volatility modeling.

So while John Hull offered some 3 examples of machine learning applied to finance (clustering to classify country risk, neural networks to model movements of the implied volatility surface and the different available methodologies for credit risk classification), Rebonato described an adaptation of Heston’s model for FX options that keeps the same set of parameters over time while providing useful information about the market price of volatility risk. This is interesting, because if such a model is a good enough approximation of the co-movements of the surface as a whole (with market implied volatilities presenting a greater volatility of volatility than their actuarial counterparts) is a good risk management tool.

Jessica James discussed the changes in borrowing, lending and hedging; the basis is not only a reality for quants, but it’s volatile enough to be monitored by the FT: https://ftalphaville.ft.com/2018/03/23/1521832181000/Cross-currency-basis-feels-the-BEAT/ . With her experience in interest rates and FX modeling, Jessica showed why some apparent opportunity can still be around: not everything can be traded in a way that enables these funding-related spreads to be captured.

Pierre Henry-Labordere provided a solid theoretical background for the application of Neural networks as universal approximators, with applications in stochastic control problems and examples for the Uncertainty Volatility Model, CVA and Initial Margin calculations.

Luca Capriotti discussed advanced AAD applications for PDE and Monte Carlo Pricing; it’s not even 10am and the number of highly regarded experts that have already spoken gives you an idea of the level of this conference.

Jim Gatheral starts from the (exact) Itô Decomposition Formula of Alòs, which decomposes option prices as the sum of: (i) the classical Black–Scholes formula with volatility parameter equal to the root-mean-square future average volatility, plus (ii) a term due to correlation and (iii) a term due to the volatility of the volatility.

By freezing the derivatives in the Alòs formula, the expected value of a derivative contract can be expressed as an exact expansion of covariance functionals; the diamond notation is used to simplify the expression of these functionals.

The relationship between these autocovariance functionals (expressed directly from the models written in forward-variance form; e.g. Bergomi-Guyon) and the covariances of terminal quantities (easily computed from simulations) allows for an easy calibration of the models.

The function ξt(T), defined as the difference between the conditional variance of the log of the asset price at T and the value of the static hedge portfolio (the log-strip) for a variance swap (it is a tradable asset) is then defined as the stochascity; it can be estimated from the volatility surface (a suitable parametrization that allows for sensible interpolations and extrapolations will still be needed, but an expression that depends on the d2 formula is available). But this function is also equal to a simple expression with two diamond operators, and because these are a function of the model parameters, the model can be calibrated directly to tradable assets without having to rely on expansions.

Trees are then used to help the computation of the diamond terms (indexing the terms and defining when a factor of 1/2 appears), being collected in forests and leading up to the Exponential Theorem, expressing the expected value of H (a solution of the Black&Scholes equation) at the terminal time T as the exponential of the (infinite) sum of the forests times the value of H today.

An important result is that writing a stochastic volatility model in forward variance model and using its characteristic function as H, itds moments can be calculated regardless of the existence of a closed form expression for the characteristic function.

The particular cases of the Bergomi-Guyon and the rough Heston models are then studied, leading to to a closed-form expression for the leverage swap in the rough Heston model, allowing for a fast calibration of the model; the leverage swap is the difference between a gamma swap and a variance swap, and a gamma swap is a weighted variance swap, with weight given by the underlying level (normalized by the initial underlying level).

The paper is available at https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2983180 and it is a must read.

Marcos López de Prado presented “Advances in financial machine learning”; the cusp of it is also available in his recent book, and the traps in strategy selection are worth going over, even if (like Michael Harris) you think that his methodology might bury strategies that are interesting.

Marco Bianchetti and Marco Scaringi use Genetic Algorithms for optimization metaheuristics in “Learning the Optimal Risk”, and were followed by Tore Opsahl (Forecasting loan utilization using neural networks).

While Lorenzo Bergomi continued his theta analysis for the case of barrier options, Peter Jaeckel presented interesting results on the use of MultiQuadric methods in “Cluster Induction”; if Peter says something about numerical methods, one should listen.

Massimo Morini presented an overview of the blockchain and discussed their practical usage on derivatives collateralization, the differences between between private and public blockchains, and many other related topics. He’s been among the first to discuss DLT at the Global Derivatives events.

I really enjoyed Jesper Andreasen’s “Tough vol” presentation. After watching the 5 rough volatility presentations last year, he embarked in a journey to understand it better, going over: (i) fractional brownian motion, rough paths, the Hurst parameter and connections to interest rate models (ii) rough volatility and its motivation (iii) asymptotic results (iv) Hawkes processes and market microstructure (v) numerical implementation.

On the motivation for rough volatility, he listed the empirical observations consistent with rough volatility and touched on a favourite topic of mine: the min variance delta, showing how rough volatility models imply a min variance delta closer to to empirical one that the standard diffusive models.

Expanding and price and implied volatility (using Alòs) he gets the ATM limits for the relevant variables, including the expected result for the time-decay of the skew (T raised to H-1/2), slower convergences for ATM deltas and digitals and flattening of the risk-reversal for short maturities.

After that he showed how Hawkes (self-exciting processes) gives rises to the behavior described on the motivation, even wothout an exogenous stochastic volatility factor, and how it might be a better approach for simulation than simulating a fractional brownian motion.

It is very interesting to see an experienced practitioner approaching a new topic and how he learns it, good enough to skip Google’s Tyler Ward presentation on Regression and information criteria, which covered the problems in applying the common regularization methods without taking into account the increase in entropy error.

Stream C had Michael Pykhtyn and Diana Iercosan, both from the FED, discussing the Basel CVA and Volcker respectively, followed by Vincent Spain from the National Bank of Belgium.

Mikko Pakkanen discussed rough volatility and its application in FX markets. Here the main problem of the rough Bergomi model is the fitting of skews at large expiries; a model that decouples skew and smile is necessary, implemented using Monte Carlo with a hybrid scheme (exact for for the first slices of the approximation of the process). Here the Monte Carlo approach can be made faster by the author’s approach of variance reduction (“Turbocharging Monte Carlo pricing for the rough Bergomi model”, available here: https://arxiv.org/abs/1708.02563 and with code here: https://github.com/ryanmccrickerd/rough_bergomi ) or by machine learning; this last approach can be controlled on a Python notebook using widgets.

At the same time, Wim Schoutens presented on derivative pricing by machine learning (please read his post here: https://knect365.com/quantminds/article/04976242-e05d-42f9-983f-09f1e78e3e82/quant-vs-machine-derivative-pricing-by-machine-learning ).

After lunch, the volatility modeling stream continued with Peter Friz on Stepping Stochvol, introducing a singular parametric Local Stochastic Volatility model (modifying Heston to allow extreme skews in the short end), with an easy implementation, followed by Laura Ballota (“Volatility by Jumps”).

Among the other presentations covering machine learning:

(i) “Learning curve dynamics with Artificial Neural Networks” by Alexei Kondratyev was interesting (especially detection of abnormal curve shapes with autoencoders)

(ii) “Machine learning and complex networks for stock market research” by Juho Kanniainen introduced the Big Data Finance project ( http://bigdatafinance.eu/ ), and “Predicting Jump Arrivals in Stock Prices Using Neural Networks with Limit Order Book Data” ( https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3165408 ) looks interesting

(iii) “From artificial intelligence to machine learning, from logic to probability” by Paul Bilokon discusses the origins of AI and machine learning, presenting the frequentist and bayesian approaches to probability and introduces domain theory as a necessary tool in the construction of partial stochastic process (there’s much more, it’s worth signing up for the Thalesians presentations).

(iv) “Deep Hedging” by Lukas Gonon: Very interesting study on learning model hedging under transaction costs, including LSTM for barrier options ( https://arxiv.org/pdf/1802.03042.pdf )

The day closed with four luminaries: Bruno Dupire with and overview of his work on volatility modeling, Damiano Brigo on risk measures for rogue traders ( check his podcast here: https://www.risk.net/comment/5389041/podcast-damiano-brigo-on-derivatives-ai-machine-learning-and-more ), Fabio Mercurio on the application of the Ito-Chaos expansion to GARCH processes and Julien Guyon on the Joint calibration of SPX and VIX options.

I missed the hacker’s presentation from Day 2, so I’ll discuss it on Day 3.

As always, any errors on the interpretation of the presentations/papers are the responsibility of Marcos. The delay is due to the sheer amount of information presented on the day, and the time needed to make justice to Jim’s presentation, which I think was the main presentation of the event if you’re interested in volatility modeling.

Tom Wolfe died yesterday; in “The Right Stuff”, there’s a contrast between the test pilots at the Edwards Air Force Base and the astronauts selected for Project Mercury; while the test pilots where in control of their planes (until they pushed the envelope too far), the astronauts were not in control of their capsules – indeed, their fate was determined by the ground control decisions, gravity and the circumstances of the launch.

In a certain way, the shift from modeling to learning evident in today’s presentations has some parallels with the right stuff … while the model designers have to deal with issues like ensuing convergence or no-arbitrage while walking the razor-thin path between tractability and explanatory power, there’s something more akin to the role of a passenger riding through an interpolated orbit as one learns its way from past data.

A good reminder of this came with the opening presentation, where Gerd Gigerenzer discussed real world heuristics vs theory and complexity. This is best exemplified by the gaze heuristic. His research program includes:

-The Adaptive Toolbox (What are the heuristics we use, their building blocks, and the evolved capacities they exploit?)

-Ecological Rationality (What types of environments does a given heuristic work in?)

-Intuitive Design (How can heuristics and environments be designed to improve decision making?)

A good anecdote about Markowitz’s own personal portfolio allocation rule (1/N) helps to bring home these points.

Stefano Pasquali (BlackRock) discussed how the machine learning framework for liquidity risk management was implemented; my favourite slides (when and how to use machine learning, a posssible application of transfer learning) are below:

The “Frontiers in big data, machine learning and supercomputing” panel had brief presentations from the debaters; some interesting points from Marcos López de Prado on the applications of machine learning in finance: hierarchical estimates instead of covariance matrices, detection of structural breaks (particularly useful in countries like Brazil, where such breaks are rather frequent), bet sizing (meta labeling), feature importance and the detection of false investment strategies; Horst Simon stressed the importance of a balanced team when working with today’s data processing challenges.

For a critical answer to López de Prado, please see Michael Harris here: https://medium.com/@mikeharrisNY/how-some-academics-misguide-traders-and-hedge-funds-b0bfd7e12a99

Alexander Giese presented on Trade Anomaly detection; I like the auto-encoder and local outlier factor approaches for finding outliers (the problem of classifying performance among a diverse – in scale – group is similar to the local outlier approach).

Lorenzo Bergomi, the author of the must-read Stochastic Volatility Modeling ( https://www.lorenzobergomi.com/ ), developed an interesting way of breaking down theta for exotic options portfolios while also pointing out that you need to work within the same Monte Carlo simulations for theta (avoid building one calculation for the price today and another – even with the same random numbers – for the price tomorrow); this is critical for longer-dated options, which have a small theta.

Vacslav Glukhov showed how JP Morgan implemented a self-learning agent with focus on limit order placement, instead of working with the traditional dynamic programming approach:

Rama Cont presented his paper “Universal Features of Price Formation in Financial Markets: Perspectives From Deep Learning” https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3141294 ; interesting results on on the model trained on all stocks outperforming the model trained on each stock.

Michael Steliaros had a lot of data the evolution of liquidity on different markets, from intraday volume profiles (please note the increasing importance and pull of the close):

To the breakdown of daily volatility into intraday vs overnight volatility:

At the same time slot, Michael Benzaquen from Écolpe Polytechnique ( http://www.off-ladhyx.polytechnique.fr/people/benzaquen/pages/publications.html ) discussed the “Recent progress in impact dynamics”; this talk featured information from “Dissecting cross-impact on stock markets: An empirical analysis” and “Unravelling the trading invariance hypothesis”.

In “Rethinking Market Impact”, Rama Cont questioned the roles that metaorder size and duration play in market impact:

An interesting day, and more commentary on these and other presentations at the end of the week.

QuantMinds 2018 (the conference formerly known as Global Derivatives) started with two summits: Quant invest and Quant Tech, with a strong presence reflecting the increasing importance and attendance of the buy side; the traditional Volatility Workshop with Bruno Dupire also happened on Monday.

The QuantReg team (Marcos, Omar and Othmane) is attending the conference; all the impressions from the summit (and any mistakes in interpreting what was presented) come from Marcos. For pictures of some of the presentations, please check his Twitter feed.

Massimo Morini opened the Quant Tech Summit by analysing how the change in the name of the conference reflects the reality: quants these days are not only working on pricing derivatives. They have been working in machine learning (some of them, like Massimo himself, worked with these statistical methods 15/20 years ago), and also on DLT and quantum computing.

Daniele Bernardi discussed some of the opportunities that fintech brings (disruption of the existing wealth management business).

Switching to the Quant Invest Summit, a great presentation from Stefano Pasquali (BlackRock) on Liquidity Risk Management, discussing how the framework for systematic risk management was implemented, the build-up of machine learning models, the measurement of slippage, etc. In my point of view, extending this framework to the PM decision making (not only the trader) will lead to a joint analysis of price and volume in portfolio allocation (it would be easier to simulate a portfolio with a realistic entry and exit prices and schedules).

Artur Sepp discussed machine learning methods (which help in dimensionality reduction) for volatility trading, with great insights on testing: avoid generalizations from results of highly path-dependent P&L calculations; test for stability and against the forecast. Look also at minimum description length / Kolmogorov complexity.

Nick Baltas discussed how the impact of crowding is context-dependent: which strategy is crowded? A risk-premia (e.g. Momentum) divergent strategy or a price anomaly (e.g. Value) convergent strategy? They might present different outcomes in terms of systemic risk (although LTCM might be an exception to this model).

Matthew Dixon discussed “Predicting Rare Events with Long Short Term Machines”; good references are his papers on this subject and this Jupyter notebook: https://github.com/Quiota/tensorflow/blob/master/TF_LSTM_LOB.ipynb

Nicolas Mirjolet showed how small/boutique hedge funds need to find the right niche of strategies (frequency of trading, etc.) and how depth (one single strategy with a Sharpe of 2.0) is better than breadth (5 strategies with individual Sharpes of 1.0 and a combined Sharpe of 2.5).

Richard Turner simulated a market model based on Farmer and Joshi 2002 ( https://pdfs.semanticscholar.org/b28d/0f8768288959cf1d85842544c46c6fe3a4af.pdf ) on “Deep Learning for Systematic Trading”.

Overall, a great day, very good presentations and interesting insights.