Mikko S. Pakkanen (photo courtesy of Oskari Ajanki)

Mikko S. Pakkanen

Senior Lecturer, Department of Mathematics, Imperial College London
Fellow, Data Science Institute
International Fellow, CREATES, Aarhus University


Department of Mathematics
Imperial College London
South Kensington Campus
London SW7 2AZ
United Kingdom

801 Weeks Building (16–18 Princes Gardens)

+44 20 7594 8541

m.pakkanen@imperial.ac.uk (work)
msp@iki.fi (personal)


I am a Senior Lecturer with the Mathematical Finance and Statistics sections in the Department of Mathematics at Imperial College London. Before joining Imperial, I was a Postdoctoral Research Fellow with CREATES at Aarhus University, Denmark and I remain affiliated with CREATES as an International Fellow. I received my PhD in Applied Mathematics and MSc in Mathematics from the University of Helsinki, Finland. To see my curriculum vitae, please click here.

My current research is focused on data science, stochastic processes and quantitative finance. My specific interests include:

I am a Fellow of the Data Science Institute and a member of the CFM–Imperial Institute of Quantitative Finance and the Stochastic Analysis Group at Imperial.


In the academic year 2021–2022, I taught the following modules at Imperial:

Enrolled students can access the teaching materials on Imperial Blackboard Learn.



Unifying incidence and prevalence under a time-varying general branching process
In collaboration with Xenia Miscouridou, Charles Whittaker, Tresnia Berah, Swapnil Mishra, Thomas A. Mellan and Samir Bhatt.
February 2022, 31 pages.
» e-print: arXiv:2107.05579

Non-average price impact in order-driven markets
In collaboration with Claudio Bellani, Damiano Brigo and Leandro Sánchez-Betancourt.
January 2022, 29 pages.
» e-print: arXiv:2110.00771

Limit theorems for the realised semicovariances of multivariate Brownian semistationary processes
In collaboration with Yuan Li and Almut E. D. Veraart.
November 2021, 35 pages.
» e-print: arXiv:2111.02366

πVAE: Encoding stochastic process priors with variational autoencoders
In collaboration with Swapnil Mishra, Seth Flaxman, Tresnia Berah, Harrison Zhu and Samir Bhatt.
August 2021, 17 pages.
» e-print: arXiv:2002.06873

Feasible inference for stochastic volatility in Brownian semistationary processes
In collaboration with Phillip Murray, Riccardo Passeggeri and Almut E. D. Veraart.
June 2021, 21 pages.
» e-print: arXiv:2007.06357, code: CRAN

Articles in refereed journals

A GMM approach to estimate the roughness of stochastic volatility
In collaboration with Anine E. Bolko, Kim Christensen and Bezirgen Veliyev.
Journal of Econometrics, to appear.
» e-print: arXiv:2010.04610

Decoupling the short- and long-term behavior of stochastic volatility
In collaboration with Mikkel Bennedsen and Asger Lunde.
Journal of Financial Econometrics, to appear.
» article: doi:10.1093/jjfinec/nbaa049, e-print: arXiv:1610.00332

State-dependent Hawkes processes and their application to limit order book modelling
In collaboration with Maxime Morariu-Patrichi.
Quantitative Finance 22(3), 563–583, 2022.
» article: doi:10.1080/14697688.2021.1983199, e-print: arXiv:1809.08060, code: GitHub

Deep hedging: Learning to remove the drift
In collaboration with Hans Buehler, Phillip Murray and Ben Wood.
Risk (March 2022), 6 pp.
» article: Risk.net, e-print: arXiv:2111.07844 (extended version)

Limit theorems for trawl processes
In collaboration with Riccardo Passeggeri, Orimar Sauri and Almut E. D. Veraart.
Electronic Journal of Probability 26, article no. 116, 36 pp., 2021.
» article: doi:10.1214/21-EJP652, e-print: arXiv:2009.10698

Hybrid simulation scheme for volatility modulated moving average fields
In collaboration with Claudio Heinrich and Almut E. D. Veraart.
Mathematics and Computers in Simulation 166, 224–244, 2019.
» article: doi:10.1016/j.matcom.2019.04.006, e-print: arXiv:1709.01310

The local fractional bootstrap
In collaboration with Mikkel Bennedsen, Ulrich Hounyo and Asger Lunde.
Scandinavian Journal of Statistics 46(1), 329–359, 2019.
» article: doi:10.1111/sjos.12355, e-print: arXiv:1605.00868

Hybrid marked point processes: characterisation, existence and uniqueness
In collaboration with Maxime Morariu-Patrichi.
Market Microstructure and Liquidity 4(3&4), 1950007, 55 pp., 2018.
» article: doi:10.1142/S2382626619500072, e-print: arXiv:1707.06970

Pathwise large deviations for the rough Bergomi model
In collaboration with Antoine Jacquier and Henry Stone.
Journal of Applied Probability 55(4), 1078–1092, 2018.
» article: doi:10.1017/jpr.2018.72, e-print: arXiv:1706.05291
» erratum: doi:10.1017/jpr.2020.109 (with Stefan Gerhold and Thomas Wagenhofer)

Turbocharging Monte Carlo pricing for the rough Bergomi model
In collaboration with Ryan McCrickerd.
Quantitative Finance 18(11), 1877–1886, 2018.
» article: doi:10.1080/14697688.2018.1459812, e-print: arXiv:1708.02563, code: GitHub

Hybrid scheme for Brownian semistationary processes
In collaboration with Mikkel Bennedsen and Asger Lunde.
Finance and Stochastics 21(4), 931–965, 2017.
» article: doi:10.1007/s00780-017-0335-5, e-print: arXiv:1507.03004

Arbitrage without borrowing or short selling?
In collaboration with Jani Lukkarinen.
Mathematics and Financial Economics 11(3), 263–274, 2017.
» article: doi:10.1007/s11579-016-0180-x, e-print: arXiv:1604.07690

On the conditional small ball property of multivariate Lévy-driven moving average processes
In collaboration with Tommi Sottinen and Adil Yazigi.
Stochastic Processes and their Applications 127(3), 749–782, 2017.
» article: doi:10.1016/j.spa.2016.06.025, e-print: arXiv:1601.03698

Functional limit theorems for generalized variations of the fractional Brownian sheet
In collaboration with Anthony Réveillac.
Bernoulli 22(3), 1671–1708, 2016.
» article: doi:10.3150/15-BEJ707, e-print: arXiv:1404.2822

Sticky continuous processes have consistent price systems
In collaboration with Christian Bender and Hasanjan Sayit.
Journal of Applied Probability 52(2), 586–594, 2015.
» article: doi:10.1239/jap/1437658617, e-print: arXiv:1310.7857

Assessing relative volatility/intermittency/energy dissipation
In collaboration with Ole E. Barndorff-Nielsen and Jürgen Schmiegel.
Electronic Journal of Statistics 8(2), 1996–2021, 2014.
» article: doi:10.1214/14-EJS942, e-print: arXiv:1304.6683

Limit theorems for power variations of ambit fields driven by white noise
Stochastic Processes and their Applications 124(5), 1942–1973, 2014.
» article: doi:10.1016/j.spa.2014.01.005, e-print: arXiv:1301.2107

On the existence of consistent price systems
In collaboration with Erhan Bayraktar and Hasanjan Sayit.
Stochastic Analysis and Applications 32(1), 152–162, 2014
» article: doi:10.1080/07362994.2014.858535, e-print: arXiv:0911.3789

Asymptotic theory for Brownian semi-stationary processes with application to turbulence
In collaboration with José Manuel Corcuera, Emil Hedevang and Mark Podolskij.
Stochastic Processes and their Applications 123(7), 2552–2574, 2013.
» article: doi:10.1016/j.spa.2013.03.011, e-print: arXiv:1211.4221

On the positivity of Riemann-Stieltjes integrals
In collaboration with Jani Lukkarinen.
Bulletin of the Australian Mathematical Society 87(3), 400–405, 2013.
» article: doi:10.1017/S0004972712000639, e-print: arXiv:1203.5276
» erratum: doi:10.1017/S0004972713000713 (included in the arXiv version)

Brownian semistationary processes and conditional full support
International Journal of Theoretical and Applied Finance 14(4), 579–586, 2011.
» article: doi:10.1142/S0219024911006747, e-print: arXiv:1002.4774

Stochastic integrals and conditional full support
Journal of Applied Probability 47(3), 650–667, 2010.
» article: doi:10.1239/jap/1285335401, e-print: arXiv:0811.1847

Microfoundations for diffusion price processes
Mathematics and Financial Economics 3(2), 89–114, 2010.
» article: doi:10.1007/s11579-010-0029-7, e-print: PDF

Articles in refereed conference proceedings

An approximative method of simulating a duel
In collaboration with Esa Lappi and Bernt Åkesson.
Proceedings of the 2012 Winter Simulation Conference (Berlin, Germany, 9–12 December 2012), pp. 2330–2339.
» article: doi:10.1109/WSC.2012.6465044

Book reviews

Review of Quantitative Trading: Algorithms, Analytics, Data, Models, Optimization by X. Guo, T. L. Lai, H. Shek and S. P. Wong
The American Statistician 72(1), 112–113, 2018.
» article: doi:10.1080/00031305.2018.1444855


Deep hedging: Learning risk-neutral implied volatility dynamics
In collaboration with Hans Buehler, Phillip Murray and Ben Wood.
Technical report, July 2021, 18 pages.
» e-print: arXiv:2103.11948

Discretization of Lévy semistationary processes with application to estimation
In collaboration with Mikkel Bennedsen and Asger Lunde.
Technical report, July 2014, 28 pages.
» e-print: arXiv:1407.2754

Mathematical aspects of financial markets with frictions
PhD dissertation in Applied Mathematics, under the supervision of Tommi Sottinen and Esa Nummelin.
Department of Mathematics and Statistics, University of Helsinki, October 2010.
» introduction available from: E-thesis

Jatkuvat semimartingaalit ja filtraation alkulaajennus
in Finnish, translated title: "Continuous semimartingales and the initial enlargement of a filtration"
MSc thesis in Mathematics, under the supervision of Tommi Sottinen.
Department of Mathematics and Statistics, University of Helsinki, October 2006.
» full text available from: E-thesis