Monte Carlo Pricing via Segmented Low-High Precision Computation
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Solution Overview
Problem
Current financial modeling systems, particularly those using Monte Carlo methods for pricing financial instruments, face challenges in achieving high accuracy while minimizing computing power and reducing power consumption, as they often require a large number of significant digits, leading to increased silicon die area and power usage.
Innovation Solution
The system employs a combination of low-precision and high-precision computations, using specialized low-power processors and single instruction multiple data (SIMD) processors to perform iterative calculations, allowing for the replacement of double-precision instructions with single-precision ones, and aggregating low-precision results to achieve high-precision accuracy with reduced computational overhead.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If high-precision (double-precision) computations are used to achieve accurate Monte Carlo simulations, then pricing accuracy is improved, but power consumption and silicon die area increase significantly
Solution Approach 1:
The patent segments the computational process into two distinct phases: a first phase using low-precision (single-precision) computations for initial Monte Carlo simulations, and a second phase using high-precision (double-precision) computations for correction. This segmentation allows the system to benefit from the efficiency of low-precision operations while ultimately achieving high-precision results, thereby reducing overall power consumption and silicon die area requirements
Solution Approach 2:
The patent applies partial high-precision action by performing only a subset of computations in double-precision (the correction phase) rather than all computations. The majority of simulations are performed in single-precision, with high-precision computations applied selectively to correct the results, thus achieving accurate pricing without the full power cost of continuous high-precision operation
2Measurement precision
If high-precision (double-precision) computations are used to achieve accurate Monte Carlo simulations, then pricing accuracy is improved, but silicon die area increases
Solution Approach 1:
The computational workflow is segmented into low-precision and high-precision phases, allowing the system to use smaller, more area-efficient single-precision arithmetic units for the majority of simulations, with double-precision units reserved only for the correction phase, thereby reducing overall silicon die area while maintaining pricing accuracy
Solution Approach 2:
The patent employs low-precision computations as a disposable, preliminary step that does not need to be highly accurate on its own, since its results will be corrected in the second phase. This allows the use of area-efficient single-precision hardware for the bulk of the computational workload
3Use of energy by moving object
If low-precision (single-precision) computations are used to reduce power consumption, then power efficiency is improved, but pricing accuracy deteriorates
Solution Approach 1:
The patent segments the computation into a power-efficient low-precision phase and a high-precision correction phase, allowing the system to achieve both power efficiency and accuracy by combining results from both phases rather than relying solely on low-precision computations
Solution Approach 2:
The low-precision computation results serve as an intermediary that is subsequently refined by high-precision correction computations. This intermediary step allows the system to leverage the efficiency of low-precision operations while using high-precision operations to eliminate accuracy errors in the final result
4Measurement precision
If a large number of Monte Carlo simulations are performed to improve pricing accuracy, then pricing accuracy is improved, but computing time increases
Solution Approach 1:
The patent performs a sufficient number of simulations in the first phase to obtain a stable estimate, then applies correction in the second phase rather than performing all simulations in high-precision. This partial use of high-precision computation reduces the total computing time required to achieve accurate results
Data Source
AI summary
This invention provides a system and method that can employ a low-instruction-per-second (lower-power), highly parallel processor architecture to perform the low-precision computations. These are aggregated at high-precision by an aggregator. Either a high-precision processor arrangement, or a low-precision processor arrangement, employing soft-ware-based high-precision program instructions performs the less-frequent, generally slower high-precision computations of the aggregated, more-frequent low-precision computations. One final aggregator totals all low-precision computations and another high-precision aggregator totals all high-precision computations. An equal number of low precision computations are used to generate the error value that is subtracted from the low-precision average. A plurality of lower-power processors can be arrayed to provide the low-precision computation function. Alternatively a plurality of SIMD can be used to alternately conduct low-precision computations for a predetermined number of operations and high-precision operations on a fewer number of operations. In an embodiment, aggregation can include summing values within predetermined ranges of orders of magnitude, via an adding tree arrangement, so that significant digits therebetween are preserved.