Abstract
PDE pricing methods such as backward and forward induction are typically implemented as unconditionally marginally stable algorithms in double precision for individual transactions. In this paper, we reconsider this strategy and argue that optimal GPU implementations should be based on a quite different strategy involving higher level BLAS routines. We argue that it is advantageous to use conditionally strongly stable algorithms in single precision and to price concurrently sub-portfolios of similar transactions. To support these operator algebraic methods, we propose some BLAS extensions. CUDA implementations of our extensions turn out to be significantly faster than implementations based on standard cuBLAS. The key to the performance gain of our implementation is in the efficient utilization of the memory system of the new GPU architecture.
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Notes
- 1.
Intel MKL library does support, Sgem2vu, an extension of Sgemv for multiplying a matrix with two vectors [3].
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Acknowledgements
The author Mohammad Zubair would like to thank Prof. Philip Treleaven, who provided him the opportunity to spend time in Spring 2014 at University College of London and interact with companies working on high performance computing for financial applications.
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Albanese, C., Regondi, P., Zubair, M. (2016). BLAS Extensions for Algebraic Pricing Methods. In: Russo, G., Capasso, V., Nicosia, G., Romano, V. (eds) Progress in Industrial Mathematics at ECMI 2014. ECMI 2014. Mathematics in Industry(), vol 22. Springer, Cham. https://doi.org/10.1007/978-3-319-23413-7_18
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DOI: https://doi.org/10.1007/978-3-319-23413-7_18
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