Multinomial Lattices and Derivatives Pricing

Jabbour, George M.; Kramin, Marat V.; Крамин, Т. В.; Young, Stephen D.

doi:10.1142/9789812565457_0001

Cited by 1 publication

(1 citation statement)

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“…The speed of convergence is determined by how well the procedures matches higher moments such as skewness and kurtosis, the higher the convergence speed, the less number of computational steps is needed to obtain a result of desired accuracy. The trinomial stencil used in the EFD method has enough degrees of freedom to match one higher moment (skewness or kurtosis) [8], although as long as the first two moments match and Equations 7 are satisfied, the stencil coefficients α, β and γ can vary while the EFD result is guaranteed to converge to the true result. Figure 3 illustrates the relationship between ∆t, ∆Z and the stencil coefficients in an EFD grid.…”

Section: Optimising Dynamic Constant Reconfigurationmentioning

confidence: 99%

Optimising explicit finite difference option pricing for dynamic constant reconfiguration

Jin

Becker

Luk

et al. 2012

22nd International Conference on Field Programmable Logic and Applications (FPL)

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This paper demonstrates a novel optimisation methodology to adjust stencil based numerical procedures from the algorithm level, so as to reduce not only the amount of hardware resource consumption per kernel but also the amount of computation required to achieve desired result accuracy, when mapping the algorithm to reconfigurable hardware using dynamic constant reconfiguration. As a result, less area is needed to support run-time reconfiguration, and less computational steps are required in the numerical procedure to obtain a result with given error tolerance. We analyse one thousand fixed point implementations on a Virtex-6 XC6V-LX760 FPGA for randomly generated option pricing problems, which are representative of industrial computation. When comparing optimised implementations to the unoptimised ones, the reconfiguration area upper bound is reduced by 22%; the average number of computational steps is reduced by 23%; and the area-computation-time product is reduced by 40%; while the numerical errors of the results are kept below the error tolerant level used in industry.

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Section: Optimising Dynamic Constant Reconfigurationmentioning

confidence: 99%