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We describe a high performance parallel implementation of a derivativepricing model, within which we introduce a new parallel method for thecalibration of the industry standard SABR (stochastic-\alpha \beta \rho)stochastic volatility model using three strike inputs. SABR calibrationinvolves a non-linear three dimensional minimisation and parallelisation isachieved by incorporating several assumptions unique to the SABR class ofmodels. Our calibration method is based on principles of surface intersection,guarantees convergence to a unique solution and operates by iterativelyrefining a two dimensional grid with local mesh refinement. As part of ourpricing model we additionally present a fast parallel iterative algorithm forthe creation of dynamically sized cumulative probability lookup tables that areable to cap maximum estimated linear interpolation error. We optimiseperformance for probability distributions that exhibit clustering of linearinterpolation error. We also make an empirical assessment of error propagationthrough our pricing model as a result of changes in accuracy parameters withinthe pricing model's multiple algorithmic steps. Algorithms are implemented on aGPU (graphics processing unit) using Nvidia's Fermi architecture. The pricingmodel targets the evaluation of spread options using copula methods, howeverthe presented algorithms can be applied to a wider class of financialinstruments.

A parallel implementation of a derivative pricing model incorporating SABR calibration and probability lookup tables