A parallel implementation of a derivative pricing model incorporating SABR calibration and probability lookup tables
We describe a high performance parallel implementation of a derivative pricing model, within which we introduce a new parallel method for the calibration of the industry standard SABR (stochastic-\alpha \beta \rho) stochastic volatility model using three strike inputs. SABR calibration involves a non-linear three dimensional minimisation and parallelisation is achieved by incorporating several assumptions unique to the SABR class of models. Our calibration method is based on principles of surface intersection, guarantees convergence to a unique solution and operates by iteratively refining a two dimensional grid with local mesh refinement. As part of our pricing model we additionally present a fast parallel iterative algorithm for the creation of dynamically sized cumulative probability lookup tables that are able to cap maximum estimated linear interpolation error. We optimise performance for probability distributions that exhibit clustering of linear interpolation error. We also make an empirical assessment of error propagation through our pricing model as a result of changes in accuracy parameters within the pricing model's multiple algorithmic steps. Algorithms are implemented on a GPU (graphics processing unit) using Nvidia's Fermi architecture. The pricing model targets the evaluation of spread options using copula methods, however the presented algorithms can be applied to a wider class of financial instruments.
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- Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
- Boyle, Phelim P., 1977. "Options: A Monte Carlo approach," Journal of Financial Economics, Elsevier, vol. 4(3), pages 323-338, May.
- Graeme West, 2005. "Calibration of the SABR Model in Illiquid Markets," Applied Mathematical Finance, Taylor & Francis Journals, vol. 12(4), pages 371-385.
- Schwartz, Eduardo S., 1977. "The valuation of warrants: Implementing a new approach," Journal of Financial Economics, Elsevier, vol. 4(1), pages 79-93, January.
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