


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

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

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)
Working Papers

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)
Presentations on seminars and conferences
 Discrete Local Volatility:
We present a discrete version of local volatility which allows finding a "closest" arbitragefree surface,
taking consistent small and large steps,
allows very efficient calculation of risk such as strike/maturitywise vega via Likelihood Greeks.
The model also distinguishes itself in that it is very robust and very easy to implement.

Discrete Local Volatility  Likelihood Ratio Risk, Affine Dividends, MultiAsset Pricing, Quanto, Stochastic Vol, Jumps
Global Derivatives Trading & Risk Mamagement Confernece, Barcelona, May 10th, 2017
We cover the basics of "Discrete Local Volatility" and describe its
use for various applications as described in the title. Examples of its superior risk
performance are provided.
This presentation is a strict superset of the below version presented in Frankfurt.

Discrete Local Volatility  Likelihood Ratio Risk, Affine Dividends, MultiAsset Pricing, Quanto
MathFinance Conference Frankfurt, April 21st, 2017
This presentation covers the basics of "Discrete Local Volatility" and describes its
use for various applications. Examples of its superior risk
performance are provided.

Discrete Local Volatility  Pricing with a Discrete Smile
Global Derivatives Trading & Risk Management Conference, Budapest, May 2016
This first presentation discusses the use of "Discrete Local Volatility" in practise
and its strenghs over classic Local Volatility. As an example, it shows how an
implied volatility surface changes under noarbitrage conditions when
switching from proportional to affine dividends.
 Statistical Hedging:
We present a novel approach to practical risk management via  essentially  regression. In contrast to classic
greek hedging, this approach makes sure
that we naturally hedge the "most risky" exposures of our portfolio. In the latest form, the idea
is basically to apply convex and monotone Markovizstyle portfolio optimization to a portfolio of derivatives.
As an application we use this approach to assess the hedging performance of different pricing models with
a focus on stochastic local volatilty. This is ongoing research.

Statistical Hedging – Cost, Carry, Risk
Global Derivatives Trading & Risk Management Conference, Amsterdam, May 2014
This presentation goes beyond the pure "meanvariance" approach in the below two presentation and uses
instead portfolio optimization under convex risk measures including transaction cost to hedge a portfolio of derivatives under liquidity constraints.
This approach is much more reasonable in practise as it provides monotone and concave pricing rules.

Statistical Hedging: Application to Stochastic Local Volatility Models
Global Derivatives Trading & Risk Management Conference, Amsterdam, May 2013
This presentation is a slimmer and updated version of the Frankfurt presentation below. It presents the idea
of statistical hedging, shows its good performance against classic greek hedging and is then applied to
Stochastic Local Vol models to assess performance differences to Local Vol. This is ongoing research.

Statistical Hedging with Stochastic Local Vol
MathFinance Conference, Frankfurt, March 2013
In this presentation we present the idea
of statistical hedging in detail. We shows its good performance against classic greek hedging, and then apply it to
Stochastic Local Vol models to assess performance differences to Local Vol. This is ongoing research.
 Stochastic Dividends:
Various presentations on how to model dividends correctly: from affine dividends over stochastic proportional dividends and
general diffusion driven models
to fully timeconsistent dividend
models. The latter is covered by 2012 Global Derivatives presentation.

Modeling Stochastic Dividends II: Consistent Cash Dividends
Global Derivatives Trading & Risk Management Conference, Barcelona, April 2012
This presentation discusses timeconsistent dividend models which allow for cashlike behaviour on
the short end and proportional dividend behaviour on the long end.

Modeling Stochastic Dividends
Global Derivatives Trading & Risk Management Conference, Paris, April 2011
This presentation discusses portional dividends and general diffusion driven dividend models and
their calibration using forward PDE methods. The section on the latter is applicable as well
to stochastic local volatility model calibration.

Modeling Dividends (JP Morgan Introduction to Quantiative Research)
Forschungsseminar Stochastische Analysis und Stochastik der Finanzmärkte
Humboldt University & Technical University, Berlin, December 2010
Covers arbitragefree handling of affine dividends and also our simple proportional dividend model.

Risk Management with Infinite Dimensional SDEs
Workshop on Computational Finance, Kyoto, August 2009

Equity Derivatives Teach In: Introduction /
Products 1 / Products 2
/ Lifecycle / Risk 1 /
Risk 2 / Numerical
Methods
Full day client teaching course, Internal JP Morgan Event, Singapore, 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, Vienna, February 2009

Hedging Options on Variance: Measuring Hedging
Performance
Global Derivatives & Risk Management, Paris, May 2007

Consistent Variance Curve Models
A sequence of presentations on consistent variance curve models, the latter discussing also fitting to an existing
curve of variance swaps. These are based mainly on the work for my PhD.

Options On Variance: Pricing And Hedging
IQPC Volatility Trading Conference, London, November 2006

Consistent Variance Curve Models
Fourth Bachelier Congress Tokyo, August 2006

Consistent Variance Curve Models, Theory and
Application
Imperial College, London, March 2006

Modeling variance swap curves: theory and
applications
Petit Déjeuner de la Finance, Frontiers in Finance, Paris, February 2006

Consistent Variance Curve Models, Theory and
Application
ISMA Centre, University of Reading, February 2006

Variance Swap Market Models
Seminar Stochastische Analysis and Stochastic der Finanzmaerkte,
Technische Universtitaet and Humboldt Universitaet Berlin, November 2005

Consistent Variance Curve Models
Seminar fuer Finanzmathematik, Technische Universtaet Wien, October 2005

Consistent Variance Curve Models
Workshop Stochastic Analysis and Applications in Finance,
Max Planck Institute Leipzig, April 2005

Valuing and Hedging Equity Derivatives
Quant Congress Europe, London, October 2005

Corridor Variance Swaps
Deutsche Bank Seminar Stochastic Analysis and Finance, May 2005

Hedging Exotic Equity Derivatives
Deutsche Bank Seminar Stochastic Analysis and Finance, Feburary 2005

Dividends in Option Pricing
Deutsche Bank Seminar Applied Numerics, August 2004

Stochastic Volatility Models and Products
Modelling techniques for pricing and hedging derivatives HK, Risk, June 2004

Levy Models in Option Pricing.
Modelling techniques for pricing and hedging derivatives London, Risk, June
2004

From Implied Volatility to Pricing Exotics
Tandem Workshop StochasticNumeric DFG, June 2004

The Heston Model
Introductory Talk TU Berlin, July 2003 (in German)

Volatilitaetsmodelle in der Praxis.
Seminar HU Berlin, May 2003 (in German)

Applying stochastic volatility models for pricing and
hedging derivatives.
Volatility Forecasting and Modelling Techniques Risk Training, NY November /
London December 2002
Introductions: Quantitative Research in der Praxis
From a long time ago
Contact
Private contact at buehler@math.tuberlin.de
(spam filter by Eleven)

