
Dr. Hans Buehler Quant of the Year 2022
hans@quantitativeresearch.de
(SSRN, Arxiv,
LinkedIn)
www.quantitativeresearch.de
Education
Employment
 19982001 Cofounder codex design software,
Berlin
 2001June 2008: Global Head of Equity Derivatives Quantitative Research,
Deutsche Bank, London; Intern to Director (2006)
 June 2008: APAC head of Equities Quantitative Research,
JP Morgan
 2010: Global Head of Equities, Sales, and Securities Services Quantitative Research (Electronic Trading & Risk Management, Financing,
Prime, Derivatives, xasset Sales, fund services,..),
JP Morgan, London; Managing Director
 Sep 2018 in addition: Global Head Equities Analytics, Automation and Optimization (AAA) at
JP Morgan, London; Managing Director, driving the transformation of the Equities business with data and analytics,
from clearing, prime through cash to derivatives.
 Summer 2022: visiting Professor TU Munich with Blanka Horvath
 From July 2022: Deputy CEO, XTX Markets.


Quant Finance 2.0  Learning To Trade
My primary focus until 2022 was the use of modern quant finance, datadriven, and AI methods for financial applications in markets with a strong focus on
reinforcement learning for execution, market making, derivatives risk management and pricing/quoting to drive client business. The use of big data and cloud compute technology
allows pushing forward the barrier from analytics, automation to optimization accross the Equities and markets businesses.
Here is my view on record:
Deep Hedging
and where we are.
Brief summary of all our papers on this area on http://deephedging.com.
My next step is to work with the leading team at XTX markets.

Books

Equity Hybrid Derivatives
(with M.Overhaus, A.Bermudez, A.Ferraris, C.Jordinson, A.Lamnouar)
The fourth book of the Deutsche Bank GME
Quantitative Products Analytics team (formerly Global Quantitiative
Research) covers a wide range equity modelling issues in general  such as
dividend handling, variance swaps, local volatility, CPPIs  and hybrid risk
from rates and credit markets.
Wiley, 2006

Volatility Markets
Revised and update version of my PhD thesis in print, incorporating new results
presented since the publication of the thesis itself, in particular on the
subject of "fitted models". A particlar section of "Fitted Heston" goes beyond
the material presented in "Equity Hybrid Derivatives".
VDM Verlag Dr. Muller, 2009
Public Commentary
Articles
Podcasts and presentations
Lectures
Patents
Published Papers

Deep Hedging: Learning to Remove the Drift
(with P.Murray, M.Pakkanen, B.Wood)
We use our Deep Hedging algorithm to construct equivalent measures which are free of "Statistical Arbitrage" in the sense that there is trading strategy which
will make money under utilitybased objective functions, i.e. we ``remove the drift". We apply this to otherwise pure ML based simulators
of option markets.
An earlier version with partial results can be found here.
Risk, Feb 2022 Risk Article

Generating Financial Markets with Signatures
(with B.Horvath, T.Lyons, I.Perez, B.Wood)
We show how a rough pathsbased feature map encoded by the signature of the path outperforms returns based
market generation both numerically and from a theoretical point of view. Finally, we also propose a suitable performance evaluation metric for financial time series and discuss some connections of our signaturebased Market Generator to deep hedging.
Risk, June 2021

Deep Hedging
in math finance notation, published in Quantitative Finance.
Version usign machine learning notation.
(with L.Gonon, J.Teichmann, B.Wood)
We present a framework for hedging a portfolio of derivatives in the presence of market frictions such as transaction costs,
liquidity constraints or risk limits using modern deep reinforcement machine learning methods. We discuss how standard reinforcement
learning methods can be applied to nonlinear reward structures, i.e. in our case convex risk measures. As a general contribution
to the use of deep learning for stochastic processes, we also show in Section 4 that the set of constrained trading strategies
used by our algorithm is large enough to eapproximate any optimal solution. Our algorithm does not depend on specific market
dynamics, and generalizes across hedging instruments including the use of liquid derivatives. Its computational performance
is largely invariant in the size of the portfolio as it depends mainly on the number of hedging instruments available.
Quantitative Finance, vol 0, num 0, 2019, pages 121
Accepted as poster sesssion at NeurIPS 2018, ICML 2019

The Heston Model (Encyclopedia
of Quantiative Finance)
(with O.Chybiryakov)
A review of the Heston model and its applications.
Encyclopedia of Quantitative Finance, Cont.R (Ed.), John
Wiley & Sons Ltd, pp. 889897 (2010)

Volatility Markets:
Consistent Modelling, Hedging and Practical Implementation
Published version of my dissertation, updated 2008
Contains extended material on consistent variance curves, a proof that "smooth"
diffusion markets are always complete, comments on pricing in local martingale
models, fitting models to the market (general, Bergomi, Dupire, Heston),
Hestontype models with semiclosed forms, algorithms to perform parameter
hedging with linear programming, computation of variance, gamma and entropy
swaps, expensive martingales, and the implementation of a particular
fourfactor variance curve model.
Defended June 26th, 2006 (summa cum laude)

Recent Developments in Mathematical Finance: A Practitioner's
Point of View
(with M.Overhaus, A.Bermudez, A.Ferraris, C.Jordinson, A.Lamnouar, A.Puthu)
An introductory text on mathematical finance which explains basic concepts and
shows applications in practise, in particular pricing of options on variance.
Covers the nature of hedging and a simple derivation of the idea of "delta
hedging".
DMV Jahresbericht, 2006 (first version May 2005)

Consistent Variance Curve Models
Generalized termstructure market model approach to variance swaps for hedging
of products on realized variance. Completeness of such models is discussed. We
also apply the results to the application recalibration of stochastic
volatility models
Finance and Stochastics, Volume 10, Number 2 / April, 2006 (first version June
2004)

Expensive Martingales
Calibration of discrete transition kernels between the marginal distributions of
a stock price process using weak information such as Cliquet prices.
The resulting onefactor process reprices spot started options and is optimized
to fit forward started options. (Generalization of DermanKani trees.)
Quantitative Finance, Volume 6, Number 3 / June 2006 (first version March 2004)

Informationequivalence: On filtrations created by
independent increments
Two Brownian motions generate the same filtration iff they are a.s.
deterministic integrals of each other (and related results).
Seminaire de Probabilites XXXVIII, p.195, Berlin, Springer 2004

Zur Struktur Brownscher Filtrationen
(in German)
A Brownian motion remains extremal on its filtration after a change of measure,
but it may not generate that filtration anymore (thesis is based on a paper by
Prof. Schachermayer; relevant new results have been published in the paper
above.)
DiplomaThesis, 2001 (1.0)
Working Papers
 Deep Bellman Hedging
(with P. Murray, B. Wood)
We present a dynamic programming "Bellman" approach to the Deep Hedging problem of hedging a portfolio of financial instruments
with other instruments, including derivatives, under market frictions. Compared to the vanilla Deep Hedging problem the approach
here attempts to learn the optimal hedging strategy for "all" portfolios across all market states.
SSRN Working paper; publication in preparation, version
1.0 June 30th 2022
 MultiAsset Spot and Option Market Simulation
(with M.Wiese, B. Wood, A. Pachoud. R. Korn. P. Murrat, L. Bai)
We construct realistic spot and equity option market simulators for a single underlying on the basis of normalizing flows. We address the highdimensionality of market observed call prices through an arbitragefree autoencoder that approximates efficient lowdimensional representations of the prices while maintaining no static arbitrage in the reconstructed surface. Given a multiasset universe, we leverage the conditional invertibility property of normalizing flows and introduce a scalable method to calibrate the joint distribution of a set of independent simulators while preserving the dynamics of each simulator. Empirical results highlight the goodness of the calibrated simulators and their fidelity.
Arxiv Working paper; publication in preparation, version
1.0 December 2021
 A DataDriven Market Simulator for Small Environments
(with B.Horvath, Terry Lyons, Immanol P. Arribas, Ben Wood)
We present a generative model based on paths signatures which is tuned towards smalldata environments commonly found in finance, and discuss various success metrics for time series simulation.
Arxiv Working paper, version
1.0 June 2020

Statistical Hedging: Motivating the Use of Convex Risk Measures for Hedging Portfolios of Derivatives Over One Time Step in the Presence of General Transaction Cost. A Summary for Derivative Quants
This note presents an extension of the generalized Markoviztype
"meanvariance" portfolio optimization approach over one period to portfolios of derivatives. Most notably, we show that once "writing off" parts of the portfolio is allowed,
we naturally arrive at using "cashinvariant monotone hulls" a'la Filipovic/Kupper to construct sensible measures of risk.
In particular, we show that the resulting riskadjusted
implementation cost function for hedging a portfolio is bounded (by the best and worst possible outcome), monotone decreasing (better portfolios are cheaper) and convex (diversification works) 
note that the classic meanvariance framework fails to satisfy the first two properties when considered over nonsymmetric returns such as those arising from working with derivatives.
This note summarizes results presented at Global Derivatives 2013 and 2014 and provides a more generalized view on the problem at hand.
This work contains little original contributions; its aim to motivate the use of convex risk measures and their construction via cashinvariant monotone hulls from a practitioner's point of view.
SSRN Working paper, version
0.931, April 2017

Discrete Local Volatility for Large Time Steps (short version) see also the
extended Version with many details, but no advanced applications.
We construct a stateandtime discrete martingale which is calibrated globally to a set of given input option prices which may
exhibit arbitrage. We also provide a method to take small steps, fully consistent with the transition kernels of the large steps.
The model's robustness vs. arbitrage violations in the input surface makes our approach particularly suited for computations
in stressed scenarios. Indeed, our method of finding a globally closest arbitragefree surface under constraints
on implied and local volatility is useful in its own right.
We demonstrate the power of our approach by showing its application to affine dividends calibrated
to option prices given by proportional dividends, availability of Likelihood Greeks,
and to meanreverting assets such as VIX. We also comment on
how to introduce jumps into our processes.
The material discussed here was also presented at Global Derivatives 2016.
SSRN Working paper. This is the first proper version of the "short"
paper after our presentation at GD'16. In particular, it discusses the incorporation
of jumps, Likelihood Greeks, and  indeed  modelling VIX with a Discrete Local Volatility process.

Volatility and Dividends II  Consistent Cash Dividends
We discuss a timehomogeneous equity stock price modelling approach with a consistent dividend process such that at any point,
conditional on the state variables of the model, shortterm implied dividends are "cashlike" (constant) and longterm dividends are "proportional".
Our approach is based on a general representation for dividend paying stocks where we prove that the stock price process is the sum of an
"inner" process plus the sum of all future appropriately discounted dividends under riskneutral measure.
This note summarizes results presented in 2012 at Global Derivatives.
We discuss dividend dynamics in the proposed approach; calibration to dividend options and the equity implied volatility surface are only touched upon as it can be acccomplished\
by standard methods.
This note summarizes results presented at Global Derivatives 2012.
SSRN Working paper, draft Version
1.00 (missing graphs), April 2012, August 25, September 9 2015

Stochastic Proportional Dividends
(with A.S.Dhouibi and D.Sluys)
Motivated by recently increased interest in trading derivatives on dividends, we present a simple, yet efficient
equity stock price model with discrete stochastic proportional dividends.
The model has a closed form for European option pricing and can therefore be calibrated efficiently
to vanilla options on the equity. It can also be simulated efficiently with MonteCarlo and has fast
analytics to aid the pricing of derivatives on dividends.
While its efficiency makes the model very appealing, it has the twin drawbacks that dividends in this model can become negative,
and that it does not price in any skew on either dividends or the stock price.
We present the model and also discuss various extensions to stochastic interest rates, local volatility and jumps.
SSRN Working paper, draft Version
1.013 December 2010 (first version January 2010, based on work from 2006 with C.Jordinson)

Volatility and Dividends  Volatility
Modelling with Cash Dividends and simple Credit Risk
This article discusses incorporating cash dividends and simple credit risk into
equity derivatives risk management. It is shown that the only consistent
way is via a simple affine transformation of the ``pure" local martingale of
the form S(t) = {F(t)  D(t)} X(t) + D(t) up to default.
Implementation and is discusseed for: plain Europeans, American options,
Barriers and finally variance swaps and related derivatives. Risk management
for volatilty hedging and variance swaps in general is discussed in detail. To
our best knowledge, this paper is the only one discussing the incorporation of
cash dividends into variance swap pricing.
The aim of the article is to present results discussed in Equity
Hybrid Derivatives in a more intuitive way (in the book all results
have been derived rigourously). It is a reference summary on volatility and
dividend modelling for equity derivatives. The updated version 1.2
contains two additional proofs compared to 1.00 from March 2009.
SSRN Working paper, version
1.3 October 2010 (first version March 2007)

Delta Hedging Works: On Market Completeness
for Diffusion Processes
This article provides new criteria for the completeness of markets driven by
diffusion processes. In particular, we show that if the coefficients of the SDE
are C^{1} almost surely, the the market of payoffs measurable with
respect to the market process is complete, regardless of the nonnegativity
of the instantaneous covariance matrix.
Our approach is in marked contrast wto the classic requirement that the
volatility matrix of the SDE is invertible in order to retrieve the background
driving motion which is much stronger and often violated in practice due to
differing trading times for underlyings in different time zones. It is also not
a very natural approach since a period of zero volatility "in one direction"
should not impede replicability in another risk factor.
SSRN Working paper, version
1.1 October 3rd, 2009 (first version March 2006)

Talks
2022 
Learning to Trade: DataDriven Quantitative Finance (plenary talk)
11th Bachelier World Congress
Hong Kong, June 2022
Learning to trade: From regression to reinforcement learning
Bloomberg Quant (BBQ) Seminar Series
February 2022

2021 
Learning to Trade
QuantMinds International
Barcelona, December 2021
Deep Hedging: Volatility Market Simulation
Risk Global Quant Network
London, July 2021
Deep Hedging: Learning RiskNeutral Market Dynamics
Oxford Newton Gateway to Mathematics, Unlocking Data Streams
Oxford, March 2021
Simulating spot and equity option markets using rough path signatures
Oxford Newton Gateway to Mathematics, Unlocking Data Streams
Oxford, March 2021

2020 
Reinforcement Learning in Trading
Risk Quant Summit London 2020
London, March 2020

2019 
Deep Hedging GAMeD: Generative Adversarial Market Dynamics for Hedging under Market Frictions
CFmImperial Quantitative Finance Seminar
London, February 2019

2018 
Deep Hedging Machinedriven trading of derivatives under market frictions
Swissquote Conference 2018 on Machine Learning in Finance
Geneva, Nov 2018
Deep Statistical Hedging
QuantMinds 2018
Lisbon, May 2018

2017 
Quant Finance: From BlackScholes To Big Data
CornellTech 10th Anniversary, Panel Discussion
New York, Nov 2017
Deep Statistical Hedging: Hedging a Portfolio of Derivatives under Transaction cost and Liquidity with Convex Risk Measures
ETH Zurich Math Finance Seminar, June 7th, 2017
University of Freiburg, Seminar, June 27th 2017
Discrete Local Volatility & Applications
Global Derivatives Trading & Risk Management Conference 2017
Barcelona, May 2017
Discrete Local Volatility:
Affine Dividends, MultiAsset Pricing, Quanto, Likelihood Risk
MathFinance Conference Frankfurt
Frankfurt, April 2017

2016 
Discrete Local Volatility: Pricing with a Discrete Smile
Global Derivatives Conference 2016
Budapest, May, 2016

2014 
Statistical Hedging – Cost, Carry, Risk
Global Derivatives Conference 2014, Amsterdam
Amsterdam, May 2014

2013 
Statistical Hedging: Application to Stochastic Local Volatility Models
Global Derivatives Conference 2013, Amsterdam
Amsterdam, May 2013
Statistical Hedging with Stochastic Local Vol
MathFinance Conference Frankfurt
Frnakfurt, March 2013

2012 
Stochastic Dividend Modeling II: Consistent Cash Dividends
Global Derivatives Trading & Risk Management Conference 2012
Barcelona, April 2012

2011 
Stochastic Dividend Modeling
Global Derivatives Trading & Risk Management Conference 2011
Paris, April 2011

2010 
Dividend Modeling
Forschungsseminar Stochastische Analysis und Stochastik der Finanzmärkte
Humboldt University, Technical University Berlin
Berlin, December 2010

2009 
Risk Management with Infinite dimensional SDEs
Workshop Computational Finance
Kyoto, August 2009
DeltaHedging Works: Market Completeness for Factor Models on the example of Variance Curve Models
Conference on small time asymptotics, perturbation theory and heat kernel
methods in mathematical finance TU Wien
Vienna, February 2009

2007 
Hedging Options On Variance
Global Derivatives & Risk Management
Paris, May 2007
Quantitative Products Analytics  Deutsche Bank’s Equity Derivatives Quant Team
University Paris 6 Student Event
Paris, January 2007

2006 
Options On Variance: Pricing And Hedging
IQPC Volatility Trading Conference
London, November 2006
Consistent Variance Curve Models
Bachelier World Congress 2006
Tokyo, August 2006
Consistent Variance Curve Models: Theory and Application
Imperial College Student Event
London, March 2006
Consistent Variance Curve Models: Theory and Application
ICMA Centre University of Reading
Reading, February 2006
Modeling Variance Swap Curves: Theory and Application
Petit Dejeuner de la Finance
Paris, February 2006

2005 
Finanzmathematik in der Praxis
Humboldt University Berlin Student Event
Berlin, December 2005
Variance Swap Market Models
Seminar Stochastische Analysis and Stochastik der Finanzmaerkte TU Berlin / HU Berlin / MATHEON
Berlin, November 2005
Valuing and Hedging Equity Derivatives
Quant Congress Europe
London, October 2005
Consistent Variance Curve Models
Technische Universität Wien
Vienna, October 2005
Consistent Variance Curve Models
Workshop Stochastic Analysis and Applications in Finance Max Planck Institute for Mathematics in the Sciences
Leipzig April 2005

2004 
Stochastic Volatility Models and Products
Risk Training Course
Hong Kong, July 2004
Construction of Martingales Under Constraints: From Implied Volatility to Pricing Exotics
TandemWorkshop StochastikNumerik TU Berlin DFG Research Centre
Berlin, June 2004
Finanzmathematik in der Praxis
Humboldt University Berlin Student Event
Berlin, June 2004
Levy Models in Option Pricing: Utilising Volatility Smile Models to Optimise Pricing and Hedging Strategies
Volatility Modelling Risk Training
London, June 2004

2003 
Volatilitätsmodelle in der Praxis
Humboldt University Berlin Student Event
Berlin, May 2003

2002 
Applying stochastic volatility models for pricing and hedging derivatives
Volatility Forecasting and Modelling Techniques Risk Training
New York, Nov 2002 and
London, Dec 2002
Quantitative Research in der Praxis
TU Berlin Student Event
Berlin, July 2002

From a long time ago
