Efficient pricing of high-dimensional (multi-assets) European Options
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.
Applied Mathematics and Computer Science
Computer, Electrical and Mathematical Sciences and Engineering
Field of Study -
Computational Finance, Computational Mathematics, Numerical Analysis
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.