Abstract
We present a highly efficient parallelization of the computation of the price of exotic cross-currency interest rate derivatives with path-dependent features via a Partial Differential Equation (PDE) approach. In particular, we focus on the parallel pricing on Graphics Processing Unit (GPU) clusters of long-dated foreign exchange (FX) interest rate derivatives, namely Power-Reverse Dual-Currency (PRDC) swaps with FX Target Redemption (FX-TARN) features under a three-factor model. Challenges in pricing these derivatives via a PDE approach arise from the high-dimensionality of the model PDE, as well as from the path-dependency of the FX-TARN feature. The PDE pricing framework for FX-TARN PRDC swaps is based on partitioning the pricing problem into several independent pricing sub-problems over each time period of the swap’s tenor structure, with possible communication at the end of the time period. Finite difference methods on non-uniform grids are used for the spatial discretization of the PDE, and the Alternating Direction Implicit (ADI) technique is employed for the time discretization. Our implementation of the pricing procedure on a GPU cluster involves (i) efficiently solving each independent sub-problem on a GPU via a parallelization of the ADI timestepping technique, and (ii) utilizing MPI for the communication between pricing processes at the end of the time period of the swap’s tenor structure. Numerical results showing the efficiency of the parallel methods are provided.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Sippel, J., Ohkoshi, S.: All power to PRDC notes. Risk Magazine 15(11), 1–3 (2002)
Piterbarg, V.V.: TARNs: Models, Valuation, Risk Sensitivities. Wilmott Magazine 14, 62–71 (2004)
Abbas-Turki, L.A., Vialle, S., Lapeyre, B., Mercier, P.: High dimensional pricing of exotic European contracts on a GPU cluster, and comparison to a CPU cluster. In: Proceedings of the 2nd International Workshop on Parallel and Distributed Computing in Finance, pp. 1–8. IEEE Computer Society (2009)
Murakowski, D., Brouwer, W., Natoli, V.: CUDA implementation of barrier option valuation with jump-diffusion process and Brownian bridge. In: Proceedings of the ACM/IEEE International Conference for High Performance Computing, Networking, Storage, and Analysis, pp. 1–4. IEEE Computer Society (2010)
Tian, Y., Zhu, Z., Klebaner, F.C., Hamza, K.: Pricing barrier and American options under the SABR model on the graphics processing units. Concurrency and Computation: Practice and Experience, 867–879 (2012)
Dang, D.M., Christara, C., Jackson, K.: Graphics processing unit pricing of exotic cross-currency interest rate derivatives with a foreign exchange volatility skew model. Journal of Concurrency and Computation: Practice and Experience (to appear, 2013), http://onlinelibrary.wiley.com/doi/10.1002/cpe.2824/abstract
Dang, D.M., Christara, C., Jackson, K.: A parallel implementation on GPUs of ADI finite difference methods for parabolic PDEs with applications in finance. Canadian Applied Mathematics Quarterly (CAMQ) 17(4), 627–660 (2009)
Dang, D.M., Christara, C., Jackson, K.: An efficient graphics processing unit-based parallel algorithm for pricing multi-asset American options. Journal of Concurrency and Computation: Practice and Experience 24(8), 849–866 (2012)
Egloff, D.: GPUs in financial computing part III: ADI solvers on GPUs with application to stochastic volatility. Wilmott, 50–53 (March 2011)
Egloff, D.: Pricing financial derivatives with high performance finite difference solvers on GPUs. In: Hwu, W.-M.W. (ed.) GPU Computing Gems Jade Edition. Applications of GPU Computing Series, pp. 309–322 (2012)
Dang, D.M., Christara, C., Jackson, K., Lakhany, A.: An efficient numerical PDE approach for pricing foreign exchange interest rate hybrid derivatives. To appear in the Journal of Computational Finance (2012), http://ssrn.com/abstract=2028519
Piterbarg, V.: Smiling hybrids. Risk Magazine 19(5), 66–70 (2006)
Gropp, W., Lusk, E., Skjellum, A.: Using MPI-2: Advanced Features of the Message Passing Interface, 1st edn. MIT Press (1999)
Andersen, L.B., Piterbarg, V.V.: Interest Rate Modeling, 1st edn. Atlantic Financial Press (2010)
Dang, D.M., Christara, C.C., Jackson, K., Lakhany, A.: A PDE pricing framework for cross-currency interest rate derivatives. In: Proceedings of the 10th International Conference in Computational Science (ICCS). Procedia Computer Sciences, vol. 1, pp. 2371–2380. Elsevier (2010)
Hull, J., White, A.: One factor interest rate models and the valuation of interest rate derivative securities. Journal of Financial and Quantitative Analysis 28(2), 235–254 (1993)
Haentjens, T., In ’t Hout, K.J.: Alternating direction implicit finite difference schemes for the Heston-Hull-White partial differential equation. Journal of Computational Finance 16(1), 83–110 (2012)
Hundsdorfer, W.: Accuracy and stability of splitting with stabilizing corrections. Appl. Numer. Math. 42, 213–233 (2002)
In ’t Hout, K.J., Welfert, B.D.: Unconditional stability of second-order ADI schemes applied to multi-dimensional diffusion equations with mixed derivative terms. Appl. Numer. Math. 59, 677–692 (2009)
NVIDIA: NVIDIA Compute Unified Device Architecture: Programming Guide Version 3.2. NVIDIA Developer Web Site (2010), http://developer.nvidia.com/object/gpucomputing.html
Dang, D.M.: Modeling multi-factor financial derivatives by a Partial Differential Equation approach with efficient implementation on Graphics Processing Units. PhD thesis, Department of Computer Science, University of Toronto, Toronto, Ontario, Canada (2011)
Harris, M., Sengupta, S., Owens, J.D.: Parallel prefix sum (scan) with CUDA. In: GPU Gems 3, pp. 851–877. NVIDIA (2007)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Dang, DM., Christara, C.C., Jackson, K.R. (2013). A Highly Efficient Implementation on GPU Clusters of PDE-Based Pricing Methods for Path-Dependent Foreign Exchange Interest Rate Derivatives. In: Murgante, B., et al. Computational Science and Its Applications – ICCSA 2013. ICCSA 2013. Lecture Notes in Computer Science, vol 7975. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39640-3_8
Download citation
DOI: https://doi.org/10.1007/978-3-642-39640-3_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-39639-7
Online ISBN: 978-3-642-39640-3
eBook Packages: Computer ScienceComputer Science (R0)