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
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, data-driven, 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.


  • 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


  • 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 non-linear 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 e-approximate any optimal solution. Our algorithm can be implemented efficiently even in high-dimensional 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 ‘complete-market’ solution.
    Quantitative Finance, vol 0, num 0, 2019, pages 1-21
  • 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)

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 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)

From a long time ago