Reduced models for sparse grid discretizations of the multi-asset Black-Scholes equation
Name
10444_2015_9421_ReferencePDF.pdf
Size
3.69 MB
Format
Adobe PDF
Checksum (MD5)
91389ec080a9854b5037ee238100a9c0
Author(s)
Gómez, Pablo
Bungartz, Hans-Joachim
Peherstorfer, Benjamin
Date Issued
May 2015
Journal
Advances in Computational Mathematics
Publisher
Springer US
Citation
Peherstorfer, Benjamin, Pablo Gómez, and Hans-Joachim Bungartz. “Reduced Models for Sparse Grid Discretizations of the Multi-Asset Black-Scholes Equation.” Adv Comput Math 41, no. 5 (May 20, 2015): 1365–1389.
Version
Author's final manuscript
Abstract
This work presents reduced models for pricing basket options with the Black-Scholes and the Heston model. Basket options lead to multi-dimensional partial differential equations (PDEs) that quickly become computationally infeasible to discretize on full tensor grids. We therefore rely on sparse grid discretizations of the PDEs, which allow us to cope with the curse of dimensionality to some extent. We then derive reduced models with proper orthogonal decomposition. Our numerical results with the Black-Scholes model show that sufficiently accurate results are achieved while gaining speedups between 80 and 160 compared to the high-fidelity sparse grid model for 2-, 3-, and 4-asset options. For the Heston model, results are presented for a single-asset option that leads to a two-dimensional pricing problem, where we achieve significant speedups with our model reduction approach based on high-fidelity sparse grid models.
MIT Department
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/s10444-015-9421-4
