


Dr. Hans Buehler
hans@quantitativeresearch.de
(SSRN,
LinkedIn)
www.quantitativeresearch.de

2001 Msc in Stochastic Analysis and Finance, Humboldt
University, thesis Zur Struktur Brownscher Filtrationen,
Prof. Hans Föllmer,
Berlin
2006 PhD in Financial Mathematics, Technical
University, thesis Volatility Markets, Prof. Alexander
Schied, Berlin
19982001 Cofounder codex design software,
Berlin
2001June 2008: Global Head of Equity Derivatives Quantitative Research,
Deutsche Bank, London; Intern to Director (2006)
June 2008: Asian Head of Equities Quantitative Research,
JP Morgan Chase, Hong Kong; Executive Director
Sep 2010: EMEA Head of Equities Quantitative Research,
JP Morgan Chase, London; Executive Director to Manging Director (2011)
Sep 2013: Global Head of Equity Derivatives Quantitative Research,
JP Morgan Chase, London; Managing Director
Aug 2014: Global Head of Equity Derivatives and Financing Quantitative Research,
JP Morgan Chase, London; Managing Director
April 2015: Global Head of Equities and Investor Services Quantitative Research (Electronic Trading & Risk Management, Financing,
Prime, and Derivatives),
JP Morgan Chase, London; Managing Director
Sep 2018 in addition: Global Head Analytics, Automation and Optimization
JP Morgan Chase, London; Managing Director

Quant Finance 2.0
My primary focus is 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. 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.

Books

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. Müller, 2009

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
Papers

Deep Hedging (Quantitative Finance)
(with L.Gonon, J.Teichmann, B.Wood)
See also our machine learning version below.
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 can be implemented efficiently even in highdimensional situations using modern machine learning tools. Its structure 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. We illustrate our approach by an experiment on the S&P500 index and by showing the effect on hedging under transaction costs in a synthetic market driven by the Heston model, where we outperform the standard ‘completemarket’ solution.
Quantitative Finance, vol 0, num 0, 2019, pages 121

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).
Séminaire de Probabilités 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)
Public Commentary
Working Papers
 Deep Hedging: Hedging Derivatives Under Generic Market Frictions Using Reinforcement Learning
(with L.Gonon, J.Kochems, B.Mohan, J.Teichmann, B.Wood)
This is the machine learning version of our Deep Hedging deep hedging paper with a few more results on applications to hedging
a portfolio of barriers.
SSRN Working paper, Version
1.0 March 2019

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)
From a long time ago

