## About me

Currently, I am a associate researcher in the CITIC research center, funded by a joint project together with the BBVA bank.
Prior, I was postdoctoral researcher in the M2NICA research group at the University of A Coruña, granted with a Juan de la Cierva-Formación fellowship.

I have obtained my BSc. degree in Computer Science at the University of A Coruña. After that,
I got an MSc. in Mathematical Engineering at the University of Vigo with specialization in
numerical techniques for mathematical finance. Then, I have worked at the Department of Mathematics
in University of A Coruña on the high-performance implementation of mathematical models with financial applications.

In 2013, I moved to The Netherlands to start my doctoral education awarded by a Marie Curie fellowship,
in the framework of an International Training Network (ITN) called STRIKE - Novel Methods in Computational Finance.
I carried out my doctoral studies at the Delft Institute of Applied Mathematics (DIAM) in the Delft University of
Technology (TU Delft) and the Scientific Computing (SC) research group of the Centrum Wiskunde & Informatica (CWI),
the National research center in mathematics and computer science in Amsterdam. Then, I was a BGSMath-María de Maeztu JUNIOR postdoctoral researcher in the Riskcenter-IREA research group
at the University of Barcelona, funded by the Barcelona Graduate School of Mathematics after competitive call.

My research topic is focused on the development of efficient numerical solution techniques in financial mathematics,
a discipline that lies at the intersection of numerical analysis and stochastic calculus. My expertise includes stochastic
processes and stochastic differential equations (SDEs), Monte Carlo methods and Fourier inversion techniques, applied to
problems appearing in the financial sector. Particularly, I am interested in hybrid solutions for advanced quantitative problems,
combining several methodologies (including computation) aiming a satisfactory balance between precision, robustness and efficiency.
My expertise also includes GPU parallel computing. Regarding my programming skills, I regularly use C, Python and Matlab.
I have taught several courses on Python programming for financial applications.

- Academic career
- Research
- Misc

## Experience

**Associate Researcher.**CITIC research centre, University of A Coruña. November 2021 - present.**Post-doc researcher.**M2NICA research group, Department of Mathematics, University of A Coruña. June 2019 - October 2021.**Teaching advisor.**Numerical Methods in Data Science, Degree of Applied Data Science, Universitat Oberta de Catalunya. February 2019 - present.**Post-doc researcher.**Riskcenter-IREA, Department of Econometrics, Statistics and Applied Economics, University of Barcelona. September 2017 - May 2019.**Researcher.**Scientific Computing research group, Centrum Wiskunde & Informatica (CWI). September 2013 - August 2017.**Researcher.**M2NICA research group, Department of Mathematics, University of A Coruña. November 2011 - September 2013.

## Education

**PhD in Applied Mathematics.**Delft University of Technology, June 2017.**University Master in Mathematical Engineering.**Official Master (90 ECTS), University of Vigo. July 2011.**University Degree in Technical Engineering of Computer Systems.**3-year official degree in Computer Science (180 ECTS), University of A Coruña. May 2010.

## Research stays

**Centrum Wiskunde & Informatica (CWI).**Scientific Computing research group, March-April 2019 (1 month).**Inria Paris.**MATHRISK research group, February 2019 (2 weeks).**Centrum Wiskunde & Informatica (CWI).**Scientific Computing research group, March 2018 (1 month).**University of Barcelona.**Financial Mathematics and Risk Control research group, Department of Econometrics, Statistics and Applied Economics, November-December 2016 (1 month).**University of A Coruña.**Models and Numerical Methods in Engineering and Applied Sciences (M2NICA) research group, Department of Mathematics, April-July 2015 (3 months).

## Supervision of students

*Deep Learning-based method for computing Initial Margin.*MSc thesis, Joel Pérez Villarino, 2021. [Repository]*Reduction of computing time for numerical pricing of European multi-dimensional options based on the COS method.*MSc thesis, Dirk Hazenoot, 2016. [Repository]

## Knowledge transfer

- Project
**Novel pricing methods for autocallables and swaptions**, in collaboration with BBVA, 2021-2022. - Participation in
**Premia platform - Pricing financial derivatives**, in collaboration with Inria Paris, 2018.

## Grants & Awards

- Juan de la Cierva-Formacion postdoctoral grant. Competitive call. [Link]
- BGSMath-María de Maeztu Junior postdoctoral grant. Competitive call. [Link]
- Marie Curie fellowship. Novel Methods in Computational Finance (ITN-STRIKE). [Link]

## Scientific & Organizing committees

- International Conference on Computational Finance 2019 (ICCF2019), 8-12 July, 2019. [Link]
- 4th BGSMath Junior Meeting, 5-6 November, 2018. [Link]

## Revision services

- Journal of Computational Finance.
- Mathematical Reviews.
- Applied Mathematics and Computation.
- SIAM Journal on Financial Mathematics.
- Journal of Computational Science.
- European Journal of Applied Mathematics.
- International Journal of Computer Mathematics.
- Mathematical Methods of Operations Research.

- Publications
- Talks & Courses
- Other

## Book

*Modelos Matemáticos y métodos numéricos en finanzas cuantitativas*, with C.W. Oosterlee and L.A. Grzelak. Aula Magna Proyecto clave McGraw Hill, 2021. [Web, Buy]

## Preprints

*Real Quantum Amplitude Estimation*, with A. Manzano and D. Musso. Submitted, 2022. [arXiv]

## Journal articles

*The stochastic θ-SEIHRD model: adding randomness to the COVID-19 spread*, with C. Vázquez. Communications in Nonlinear Science and Numerical Simulation 115, 2022. [Journal, arXiv]*On a neural network to extract implied information from American options*, with S. Liu, A. Borovykh and C.W. Oosterlee. Applied Mathematical Finance: 1-27, 2022. [Journal, arXiv]*A survey on quantum computational finance for derivatives pricing and VaR*, with A. Gómez, A. Manzano, D. Musso, M. Rodríguez-Nogueiras, G. Ordóñez and C. Vázquez. Archives of Computational Methods in Engineering, 2022. [Journal, Repository]*A modular framework for generic quantum algorithms*, with A. Manzano, D. Musso, A. Gómez, G. Ordóñez, M. Rodríguez-Nogueiras and C. Vázquez. Mathematics 10(5), 785, 2022. [Journal, arXiv]*The CTMC-Heston model: calibration and exotic option pricing with SWIFT*, with J.L. Kirkby and L. Ortiz-Gracia. Journal of Computational Finance 24(4): 71-114, 2021. [Journal, SSRN]*Nonparametric density estimation and bandwidth selection with B-spline bases: a novel Galerkin method*, with J.L. Kirkby and D. Nguyen. Computational Statistics and Data Analysis 159, 2021. [Journal, SSRN]*Model-free computation of risk contributions in credit portfolios*, with L. Ortiz-Gracia. Applied Mathematics and Computation 382, 2020. [Journal, SSRN]*Rolling Adjoints: Fast Greeks along Monte Carlo scenarios for early-exercise options*, with S. Jain and C.W. Oosterlee. Journal of Computational Science 33: 95-112, 2019. [Journal, SSRN]*BENCHOP–SLV: The BENCHmarking project in Option Pricing – Stochastic and Local Volatility problems*, with L. von Sydow, S. Milovanović, E. Larsson, K. In't Hout, M. Wiktorsson, C.W. Oosterlee, V. Shcherbakov, M. Wyns, S. Jain, T. Haentjens and J. Waldén. International Journal of Computer Mathematics 96(10): 1910-1923, 2019. [Journal]*SWIFT valuation of discretely monitored arithmetic Asian options*, with L. Ortiz-Gracia and E.I. Wagner. Journal of Computational Science 28: 120-139, 2018. [Journal, SSRN]*On the data-driven COS method*, with C.W. Oosterlee, L. Ortiz-Gracia and S.M. Bohte. Applied Mathematics and Computation 317: 68-84, 2018. [Journal, SSRN]*On an efficient multiple time step Monte Carlo simulation of the SABR model*, with L.A. Grzelak and C.W. Oosterlee. Quantitative Finance 17(10): 1549-1565, 2017. [Journal, SSRN]*On a one time-step Monte Carlo simulation approach of the SABR model: Application to European options*, with L.A. Grzelak and C.W. Oosterlee. Applied Mathematics and Computation 293: 461-479, 2017. [Journal, SSRN]*GPU acceleration of the Stochastic Grid Bundling Method for early-exercise options*, with C.W. Oosterlee. International Journal of Computer Mathematics 92(12): 2433-2454, 2015. [Journal, SSRN]*Static and dynamic SABR stochastic volatility models: calibration and option pricing using GPUs*, with J.L. Fernández, A.M. Ferreiro, J.A. García, J.G. López-Salas and C. Vázquez. Mathematics and Computers in Simulation 94: 55-75, 2013. [Journal]

## Talks & Courses

*Neural Networks for extracting implied information from American options*, 10th June, 2022 at International Conference on Computational Finance, ICCF 2022, Wuppertal. [Slides]*Neural Networks for extracting implied information from American options*, 14th June, 2021 at 26th CEDYA/16th CMA, Xixón. [Slides]*A stochastic θ-SEIHRD model: adding randomness to the COVID-19 spread*, 18th December, 2020 at 8th COVID-19 Webinar. [Slides, YouTube]*Machine Learning to compute implied volatility from European/American options considering dividend yield*, 9th October, 2020 at 3rd XoveTIC conference, A Coruña. [Slides]*Continuous Time Markov Chain approximation of the Heston model*, 19th July, 2019 at International Conference on Computational Finance, ICCF 2019, A Coruña. [Slides]*Crash course on Python programming*, 4-5th July, 2019 at University of A Coruña, A Coruña. [Slides]*Model-free computation of risk contributions in credit portfolios*, 27th May, 2019 at Seminar Riskcenter IREA-UB, University of Barcelona. [Slides]*Efficient one and multiple time-step simulation of the SABR model*, 7th February, 2019 at MATHRISK seminar, CERMICS laboratory, Paris. [Slides]*The Asian SWIFT method*, 19th December, 2018 at Seminar Finance-UB, University of Barcelona. [Slides]*GPU acceleration in early-exercise option valuation*, 26th September, 2018 at Financial Mathematics and Supercomputing, A Coruña. [Slides]*The Asian SWIFT method*, 10th July, 2018 at International Conference on Computational and Mathematical Methods in Science and Engineering, CMMSE 2018, Rota. [Slides]*Rolling Adjoints: Fast Greeks along Monte Carlo scenarios for early-exercise options*, 16th May, 2018 at QuantMinds International 2018, Lisbon. [Slides]*Rolling Adjoints: Fast Greeks along Monte Carlo scenarios for early-exercise options*, 20th March, 2018 at Reading group. Centrum Wiskunde & Informatica (CWI), Amsterdam. [Slides]*Monte Carlo-based methods for the BENCHOP project*, 22nd September, 2017 at Applied Mathematics Techniques for Energy Markets in Transition, Lorentz workshop 2017, Leiden. [Slides]*The data-driven COS method*, 6th July, 2017 at International Conference on Computational and Mathematical Methods in Science and Engineering, CMMSE 2017, Rota. [Slides]*The BENCHmarking project in Option Pricing*, 19th June, 2017 at Reading group. Centrum Wiskunde & Informatica (CWI), Amsterdam. [Slides]*Efficient one and multiple time-step simulation of the SABR model*, 20th April, 2017 at MathFinance conference 2017, Frankfurt. [Slides]*The data-driven COS method*, 13th March, 2017 at Reading group. Centrum Wiskunde & Informatica (CWI), Amsterdam. [Slides]*The data-driven COS method*, 2nd December, 2016 at Faculty of Economics. University of Barcelona. [Slides]*Crash course on Python programming: Python for computational finance*, 1st July, 2016 at Summer school on quantitative methods for risk management in finance and insurance, SSQM 2016, A Coruña. [Slides]*Efficient one and multiple time-step simulation of the SABR model*, 14th June, 2016 at Minisymposium: Computational methods for finance and energy markets, ECMI 2016, Santiago de Compostela. [Slides]*Pricing early-exercise options: GPU Acceleration of SGBM method*, 6th April, 2016 at SIAM conference on Uncertainty Quantification, UQ 2016, Lausanne. [Slides]*Efficient one and multiple time-step simulation of the SABR model*, 15th February, 2016 at Reading group. Centrum Wiskunde & Informatica (CWI), Amsterdam. [Slides]*Stochastic Grid Bundling Method: GPU Acceleration*, 17th December, 2015 at International Conference on Computational Finance, ICCF 2015, London. [Slides]*Stochastic Grid Bundling Method: GPU Acceleration*, 7 of July, 2015 at Stochastics & Computational Finance - from academia to industry, SCF 2015, Lisbon. [Slides]*Parallel computing with Python*, 10th December, 2014 at Python for finance - an Introduction. ISEG, Lisbon. [Slides]*On a GPU Acceleration of the Stochastic Grid Bundling Method*, 13th June, 2014 at Young Researchers' Minisymposium: High Performance Computational Finance, ECMI 2014, Taormina. [Slides]*Static and dynamic SABR model*, 18th November, 2013 at Reading group, Centrum Wiskunde & Informatica (CWI), Amsterdam. [Slides]

## Doctoral thesis

*Hybrid Monte Carlo methods in Computational Finance.*Delft University of Technology, July 2017. [Repository, Slides]

## Chapters in books

*A Highly Efficient Numerical Method for the SABR Model*, with Lech A. Grzelak and C.W. Oosterlee. Novel Methods in Computational Finance, 2017. [Link]*Modern Monte Carlo Methods and GPU Computing*, with C.W. Oosterlee. Novel Methods in Computational Finance, 2017. [Link]

## Conference proceedings

*Quantum Arithmetic for Directly Embedded Arrays*. In Proceedings of the 4th XoveTIC conference, 2021. [Link]*Deep Learning-Based Method for Computing Initial Margin*. In Proceedings of the 4th XoveTIC conference, 2021. [Link]*Machine Learning to Compute Implied Volatility from European/American Options Considering Dividend Yield*. In Proceedings of the 3rd XoveTIC conference, 2020. [Link]*SWIFT valuation of discretely monitored arithmetic Asian options under exponential Lévy processes*. In Proceedings of the 18th International Conference on Computational and Mathematical Methods in Science and Engineering, 2018. [Link]*The data-driven COS method*. In Proceedings of the 17th International Conference on Computational and Mathematical Methods in Science and Engineering, 2017. [Link]*Efficient multiple time-step simulation of the SABR model*. In Proceedings of the 19th European Conference on Mathematics for Industry, 2016, Springer Heidelberg. [Link]*On a GPU acceleration of the Stochastic Grid Bundling Method*. In Proceedings of the 18th European Conference on Mathematics for Industry, 2014, Springer Heidelberg. [Link]

## Contact

CITIC research center

University of A Coruña

Campus de Elviña s/n

15071 A Coruña, Spain

e-mail: alvaro.leitao AT udc.es

## Research profiles