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Efficient pricing of high-dimensional (multi-assets) European Options

Project

Project Details

Program
Applied Mathematics and Computer Science
Field of Study
Computational Finance, Computational Mathematics, Numerical Analysis
Division
Computer, Electrical and Mathematical Sciences and Engineering
Faculty Lab Link
https://www.kaust.edu.sa/en/study/faculty/raul-tempone

Project Description

The student will work on designing new numerical methods based on hierarchical adaptive sparse grids quadratures combined with Fourier techniques for efficient pricing of high-dimensional (multi-assets) European Options. Specifically, the student will contemplate the possibility of finding a heuristic framework for an optimal choice of the integration contour (damping parameter) which controls the analyticity of the integrand in the Fourier space and hence accelerate the performance of the quadrature methods. He will also develop a systematic comparison between hierarchical deterministic quadrature methods, Tensor Product (TP) quadrature, Smolyak (SM) Sparse Grids quadrature, and Adaptive Sparse Grids (ASG) quadrature to numerically evaluate the option price under different pricing dynamics, Geometric Brownian Motion (GBM), Variance Gamma (VG) and Normal Inverse Gaussian (NIG) for different multi-asset payoff functions such as Basket Call/Put and Rainbow options. The student is also asked to elaborate a comparison in terms of computational complexity against the quadrature methods for different dimensions, and various combination of parameter sets within the mentioned pricing models.

About the Researcher

Raul Tempone
Professor, Applied Mathematics and Computational Science
Computer, Electrical and Mathematical Science and Engineering Division

Affiliations

Education Profile

  • Ph.D. Numerical Analysis, Royal Institute of Technology, 2002
  • M.S. Engineering Mathematics, Universidad de la Republica, Montevideo, Uruguay, 1999
  • B.S. Industrial and Mechanical Engineering, Universidad de la Republica, Montevideo, Uruguay, 1995

Research Interests

Raul Tempone's research interests are in the mathematical foundation of computational science and engineering. More specifically, he has focused on a posteriori error approximation and related adaptive algorithms for numerical solutions of various differential equations, including ordinary differential equations, partial differential equations, and stochastic differential equations. He is also interested in the development and analysis of efficient numerical methods for optimal control, uncertainty quantification and bayesian model calibration, validation and optimal experimental design. The areas of application he considers include, among others, engineering, chemistry, biology, physics as well as social science and computational finance.

Selected Publications

  • Hoel, H., Shaimerdenova, G., & Tempone, R. (2022). Multi-index ensemble Kalman filtering. Journal of Computational Physics, 111561.
  • Cramer, E., Mitsos, A., Tempone, R., & Dahmen, M. (2022). Principal component density estimation for scenario generation using normalizing flows. Data-Centric Engineering, 3.
  • Kiessling, J., StrA¶m, E., & Tempone, R. (2021). Wind field reconstruction with adaptive random Fourier features. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 477(2255). doi:10.1098/rspa.2021.0236
  • Espath, L., Kabanov, D., Kiessling, J., & Tempone, R. (2021). Statistical learning for fluid flows: Sparse Fourier divergence-free approximations. Physics of Fluids, 33(9), 097108. doi:10.1063/5.0064862
  • Nadhir Ben Rached, Abla Kammoun, Mohamed-Slim Alouini, Raul Tempone , On the Efficient Simulation of Outage Probability in a Log-normal Fading Environment,IEEE Transactions on Communications 65 Issue: 6, 2017
  • F. Ruggeri, Z. Sawlan, M. Scavino, R. Tempone, A hierarchical Bayesian setting for an inverse problem in linear parabolic PDEs with noisy boundary conditions, Bayesian Analysis, Advance Publication, 12 May 2016. doi: 10.1214/16-BA1007
  • C. Bayer, J Happola, R. Tempone, Implied Stopping Rules for American Basket Options from Markovian Projection, arXiv:1705.00558v1, May 2017
  • A. Haji-Ali, R. Tempone, ""Multilevel and Multi-index Monte Carlo methods for the McKean-Vlasov equation"", has been accepted for publication in Statistics and Computing. 20
  • M. Iglesias, Z. Sawlan, M. Scavino, R. Tempone, C. Wood, Bayesian inferences of the thermal properties of a wall using temperature and heat flux measurements, accepted for publication in International Journal of Heat and Mass Transfer, Sep. 2017

Desired Project Deliverables

As the main project deliverable, we expect a scientific report (eventually a research manuscript) including a detailed description and analysis of the proposed methodology developed within the course of the internship and providing all numerical experiments to showcase the versatility of the proposed heuristic framework. The working environment the student will use should include a GIT repository shared with the project collaborators in which he includes all project-related materials such as progress reports, codes, figures, and important references from the literature to facilitate the supervision task and communicate ideas more effectively.

Recommended Student Background

Code development and software engineering skills, such as Matlab and/or Python.
Education in applied mathematics or equivalent
Education and possibly experience in the field of Financial Engineering and/or Stochastic Numerics
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3-6 months
Internship period
100+
Research Projects
3.5/4
Cumulative GPA
310
Interns a Year