Dr. Hans Buehler
hans@quantitative-research.de (SSRN, LinkedIn)


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

1998-2001 Co-founder codex design software, Berlin
2001-June 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


  • 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


  • 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. 889-897 (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), Heston-type models with semi-closed forms, algorithms to perform parameter hedging with linear programming, computation of variance, gamma and entropy swaps, expensive martingales, and the implementation of a particular four-factor 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 term-structure 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 re-calibration 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 one-factor process reprices spot started options and is optimized to fit forward started options. (Generalization of Derman-Kani trees.)

    Quantitative Finance, Volume 6, Number 3 / June 2006 (first version March 2004)
  • Information-equivalence: 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.)
    Diploma-Thesis, 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 Markoviz-type "mean-variance" 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 "cash-invariant monotone hulls" a'la Filipovic/Kupper to construct sensible measures of risk. In particular, we show that the resulting risk-adjusted 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 mean-variance framework fails to satisfy the first two properties when considered over non-symmetric 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 cash-invariant 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 state-and-time 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 arbitrage-free 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 mean-reverting 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 time-homogeneous equity stock price modelling approach with a consistent dividend process such that at any point, conditional on the state variables of the model, short-term implied dividends are "cash-like" (constant) and long-term 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 risk-neutral 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 Monte-Carlo 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 C1 almost surely, the the market of payoffs measurable with respect to the market process is complete, regardless of the non-negativity 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" arbitrage-free surface, taking consistent small and large steps, allows very efficient calculation of risk such as strike/maturity-wise vega via Likelihood Greeks. The model also distinguishes itself in that it is very robust and very easy to implement.
  • 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 Markoviz-style portfolio optimization to a portfolio of derivatives.
    This is on-going research.

    • Deep Statistical Hedging
      ETH Zurich June 7th, 2017; University of Freiburg, June 27th 2017
      Hedging of derivatives under transaction cost and liquidity constraints using modern deep reinforcement learning techniques.
    • Statistical Hedging – Cost, Carry, Risk
      Global Derivatives Trading & Risk Management Conference, Amsterdam, May 2014
      This presentation goes beyond the pure "mean-variance" 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 on-going 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 on-going 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 time-consistent 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 time-consistent dividend models which allow for cash-like 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 arbitrage-free 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
  • Delta-Hedging 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.    
  • 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 Stochastic-Numeric 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


Private contact at buehler@math.tu-berlin.de (spam filter by Eleven)