The Role of FPGAs in Modern Option Pricing Techniques: A Survey
Abstract
:1. Introduction
2. Methodology
2.1. Search Strategy
2.2. Inclusion and Exclusion Criteria
2.3. Data Extraction
- Black–Scholes Model
- Binomial and Trinomial Tree Methods
- Monte Carlo Simulations
- Finite Difference
- Heston Model
- Quadrature Methods
- Miscellaneous
3. Comparison of FPGA, CPU, and GPU
4. Review of FPGA Implementations for Option Pricing
4.1. Black–Scholes Model
4.1.1. Black–Scholes Model on FPGA
4.1.2. Key Observations
4.2. Binomial and Trinomial Tree Methods
4.2.1. Binomial and Trinomial Tree Methods on FPGA
4.2.2. Key Observations
4.3. Monte Carlo Simulations
4.3.1. Monte Carlo Simulations on FPGA
4.3.2. Key Observations
4.4. Finite Difference
4.5. Finite Difference on FPGA
Key Observations
4.6. Heston Model
4.6.1. Heston Model on FPGA
4.6.2. Key Observations
4.7. Quadrature Methods
4.7.1. Quadrature Methods on FPGA
4.7.2. Key Observations
4.8. Miscellaneous Models
Key Observations
5. Challenges and Future Directions
5.1. Challenges
5.2. Future Directions
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Aspect | FPGA | CPU | GPU |
---|---|---|---|
Consumption | Low to Moderate | Moderate to High | High |
Computing Power | High (specific tasks) | Moderate (general) | Very High (parallel tasks) |
Flexibility | High (custom hardware) | Very High (general) | Moderate (parallel optimized) |
Latency | Very Low | Moderate | Low to Moderate |
Programming | Complex (hardware knowledge) | Easy (high-level languages) | Moderate (requires parallelism) |
Development Time | Long (custom design) | Short (established tools) | Moderate (specialized tools) |
Cost | High (initial, low volume) | Low to Moderate | Moderate to High |
Parallelism | High (custom pipelines) | Low to Moderate | Very High |
Use Case | Specialized, real-time | General-purpose | Parallel processing, AI/ML |
Study | Notable Findings |
---|---|
Tandon (2003) [17] | Implemented Black–Scholes on Xilinx Virtex-II Pro, achieving a 3400× speedup over ARM processor and 312× over Mathematica. |
Baxter et al. (2007) [18] | FPGA-based pricing model for ‘Asian’ options, showing a 270× speedup for a single FPGA and 5400× for 16 FPGAs compared to a Xeon blade CPU. |
Thomas et al. (2007) [19] | Hardware architecture for generating random vectors for Delta-Gamma Value-at-Risk and Black–Scholes, achieving 200× the generation rate of a single Opteron 2.2 GHz CPU. Equivalent to 33 quad-core CPUs. |
Bruce (2008) [11] | Implemented Black–Scholes–Merton options pricing on various hardware platforms, estimating a 298× speedup for Black–Scholes. Highlighted interconnect limitations for both GPU and FPGA. |
Castillo et al. (2009) [20] | SMILE architecture with 32 nodes, 5× faster than a traditional computing cluster with the same number of nodes. Traditional cluster needs 256 processors to match SMILE’s response times. |
Patel et al. (2016) [21] | OpenCL-based kernel for European Stock Option pricing on FPGA, significantly outperforming CPU and GPU architectures, achieving computational times in milliseconds. |
Choo et al. (2013) [22] | High-performance Black–Scholes system on Altera Stratix-V FPGA for pricing European call options. |
Inggs (2015) [2] | Demonstrated HLS tools’ industrial readiness for Black–Scholes and Heston models, achieving up to 221× speedup over sequential CPU implementation. |
Guerrero et al. (2015) [23] | Structured product pricer on FPGA, achieving speed-ups of 550 to 1450 times compared to a one-core software solution. |
Pham et al. (2016) [24] | Design flow for efficient hardware accelerators for option pricing on FPGA, outperforming most manually-designed engines and software implementations by 2×. |
Inggs (2016) [25] | Emphasized power efficiency improvements (30% more floating point operations per Joule of energy) in computational finance on FPGA. |
Ma (2019) [26] | FPGA-based accelerators for computational finance, achieving 4× to 5× more operations per Watt than GPU. |
Rodrigues et al. (2019) [28] | Specialized architectures for financial product pricing on FPGA, providing a speedup of 550× to 1450×. |
de Castro (2019) [27] | results indicated inefficiencies (slowdown) in the FPGA solution compared to a Python execution on the ARM. |
Li et al. (2021) [29] | Efficient hardware structure for Black–Scholes on FPGA, showing a 365× speedup over CPU implementations and 2.6× over GPU. Throughput-power efficiency speedup of 3293× compared to CPU and 59.4× compared to GPU. |
Wang et al. (2022) [30] | Parallelized framework for computing implied volatility on FPGA, showing 4× to 5× speedup over traditional methods. |
Study | Notable Findings |
---|---|
Morales et al. (2014) [32] | FPGA implementation evaluated over 2000 options/s with <20 W power consumption. |
Jin et al. (2008) [33] | 250× faster than Core2 Duo, 2× faster than Nvidia Geforce 7900GTX. |
Wynnyk and Magdon-Ismail (2009) [34] | 73× speedup over optimized CPU implementation. |
Jin et al. (2009) [35] | 100× faster than Core2 Duo, 2× faster than non-CUDA Nvidia GPU, 6× more efficient in power consumption. |
Chatziparaskevas et al. (2012) [36] | 5× speedup compared to 2 GHz dual-core Intel CPU. |
Tavakkoli et al. (2014) [38] | 65× improvement in option latency |
Fabry et al. (2017) [37] | 50× improvement in throughput for Monte Carlo option pricing. |
Morales et al. (2014) [32] | 5× more energy efficient than software implementation. |
Tavakkoli et al. (2017) [39] | 1.4× throughput vs. hand-tuned systolic design, up to 9.1× and 5.6× improvement vs. scalar and vector architectures. |
Minhas et al. (2018) [40] | 68% device peak performance for FPGA vs. 20% for NVIDIA GPU, up to 1.4× energy efficiency improvement. |
Mahony et al. (2020) [10] | Two-asset European option pricer, 25× latency reduction, 39.3 W power consumption. |
Mahony et al. (2022) [7] | Multi-asset option pricer, 43× faster than software-based general-purpose processor. |
Study | Notable Findings |
---|---|
Zhang et al. (2005) [42] | Hardware accelerator achieving 50× speedup for financial applications. |
Anlauf (2005) [43] | 12× speedup for Monte Carlo simulations on FPGAs. |
Bower et al. (2006) [44] | Modular framework with speedups between 8× to 71×. |
Morris et al. (2007) [45] | ‘HyperStreams’ abstraction, 146× acceleration for European option pricing. |
Tian et al. (2008) [46] | Monte Carlo engine, 340× to 750× speedup. |
Tian and Benkrid (2009) [48] | LSMC method for American options, 20× speedup and >20:1 energy savings. |
Woods et al. (2008) [49] | QMC derivative pricing, 50× performance over 3 GHz processor. |
Tian et al. (2012) [50] | LSMC method, 25× path generation, 18× regression, 20× overall, 54× energy efficiency. |
Thomas (2010) [51] | Contessa language, up to 62× speedup, significant power savings. |
Anson et al. (2010) [52] | Dynamic scheduling, 44× speedup, 19.6× energy efficiency. |
Tian et al. (2010) [53] | Fixed-point arithmetic, enhanced throughput with negligible error. |
De Schryver et al. (2011) [54] | Heston model accelerator, 89% energy savings, 2× speedup. |
Hegner et al. (2012) [55] | ASP-4P configuration, 3686× energy efficiency. |
Diamantopoulos et al. (2021) [56] | CloudiFi framework, up to 485× improvement. |
Liu et al. (2010) [57] | 690× faster for intensive tasks on FPGA-based cluster. |
Tian et al. (2010) [58] | Interest rate derivative pricing, 58× speedup, more energy efficient. |
Betkaoui et al. (2010) [60] | Comparative study, FPGA 4× greater power efficiency than Intel Xeon. |
Chow et al. (2012) [61] | Mixed precision, 170× speedup, significant energy efficiency improvements. |
De Schryver et al. (2013) [62] | Multi-level Monte Carlo, 50% complexity reduction, <3.6 W power. |
Jin (2013) [63] | Reconfigurable hardware, 28× to 149× speedup, 18.6× energy efficiency. |
De Schryver et al. (2014) [72] | 800× speed advantage, 2.8× lower power consumption. |
Jong (2014) [66] | 4200× speed up over CPU |
Omland et al. (2015) [67] | MLMC simulations, 3–9× speed-up. |
Choi et al. (2016) [68] | High-level synthesis, 3.89× speedup for Black–Scholes. |
Lomuscio et al. (2016) [69] | Dynamic loading, 30× to 120× speedup, up to 30× energy efficiency. |
Muslim et al. (2017) [70] | High-level synthesis, 2× speedup, significant power efficiency. |
Setetemela et al. (2018) [71] | High-level FPGA design toolflow. |
Brugger et al. (2014) [72] | HyPER, 3.4× faster, 36× more power efficient. |
Toft et al. (2014) [73] | Monte Carlo simulation on Xilinx Virtex-5, 46.2× speedup, 14.4× energy efficiency. |
Study | Notable Findings |
---|---|
Jin et al. (2011) [75] | 24× speed increase using Virtex-6 FPGA. |
Jin et al. (2009) [76] | 12× speed of Pentium 4, 9.4× more energy-efficient than GPU on xc4vlx160 FPGA. |
Becker et al. (2011) [77] | Dynamic reconfiguration on Virtex-6 XC6VLX760, 4.7× speed-up for partial reconfiguration. |
Albicocco et al. (2012) [78] | Combined FPGA and CPU system consuming less than 1/100th of the energy of CPU alone. |
Study | Notable Findings |
---|---|
De Schryver et al. (2011) [80] | Detailed methodology for designing and evaluating optimal hardware accelerators for the Heston model; introduced new hardware random number generator and accelerator for European barrier option prices. |
Stumm (2013) [81] | Comparative study between Chisel and VHDL for the Heston Model; 30% reduction in code size with Chisel, but challenges with floating point support and XILINX IP cores. |
Wu et al. (2014) [82] | Heterogeneous computing platform integrating GPU and FPGA; analyzed Heston Model for option pricing; FPGA 1.84 × Ops/Joule efficiency compared to GPU. |
Klaisoongnoen et al. (2022) [83] | Applied Heston model on Xilinx Alveo U280 FPGA; 8 to 185 times performance improvement over two 24-core Intel Xeon Platinum CPUs; 2.6379 × Ops/Joule power efficiency. |
Study | Notable Findings |
---|---|
Anson (2009) [85] | FPGA architecture for complex options pricing; 32.8× speedup and 8.3× power efficiency over Tesla C1060 GPU. |
Jin (2009) [86] | Automated hardware accelerators for European options via quadrature method; 18× faster and 143× more power efficient (single precision); 7× faster and 77× more power efficient (double precision) than Pentium 4. |
Anson (2011) [87] | Parallel architecture for multi-dimensional options; Virtex-4 xc4vlx160 FPGA 4.6× faster and 25.9× more energy-efficient than Xeon W3504 dual-core CPU; 2.6× faster and 25.4× more energy-efficient than a comparable GPU. |
Tse (2012) [88] | Precision optimization for quadrature computation; up to 6× faster than FPGA designs with double precision; 15.1× faster and 234.9× more energy-efficient than i7-870 CPU; 1.2× faster and 42.2× more energy-efficient than Tesla C2070 GPU. |
Study | Notable Findings |
---|---|
Kaganov et al. (2008) [89] | CDO pricing using OFGC model; 63× faster than software on Intel Xeon. |
Kaganov et al. (2011) [91] | One-Factor and Multi-Factor Gaussian Copula models; 64–71× faster than software on Intel Xeon. |
Thomas et al. (2008) [92] | Generating vectors for modeling correlations; 26× faster than quad Opteron 2.6 GHz SMP. |
Saiprasert et al. (2010) [93] | MVGRNG for VaR estimation; up to 96% improvement in performance. |
Stamoulias et al. (2017) [94] | Hardware accelerators for risk valuation; Black–Scholes and Black-76 up to 348× and 297× faster, Binomial up to 38× faster. |
Ma et al. (2016) [95] | Black–Scholes and Heston models; FPGA 5.9%-9.8% energy per computation, 1.71–2.56× faster than GPU. |
Varela et al. (2015) [96] | Multi-dimensional American options on CPU/FPGA; 2× speedup, Zynq FPGA consumes only 7 kJ vs. 614 kJ for Atom. |
Nestorov et al. (2017) [98] | Asian option pricing on HPC; 4–9.2× speedup, 45× power efficiency improvement. |
Peverelli et al. (2018) [99] | OXiGen tool for FPGA-based kernels; 88.1× speedup over single-threaded software. |
Ibraev (2020) [101] | Gaussian Copula Model acceleration; 4× speedup compared to CPU. |
Morris et al. (2009) [103] | Market data feed processing; 12× improvement over real-world rate. |
Lockwood et al. (2012) [104] | FPGA IP libraries for electronic trading; 2× latency reduction, Celoxica AMDC accelerator card < 15 W power. |
Leber et al. (2011) [105] | High Frequency Trading applications; 4× latency reduction vs. software. |
Del Sozzo et al. (2023) [106] | Senju automation framework for ISLs; potential applications in financial data processing. |
Lázaro García (2013) [107] | HPC approach for predicting market trends; significant speedup for options. |
Palmer (2014) [108] | FPGA-based tridiagonal solver; 36× speedup (fixed-point), 16× speedup (floating-point), 16× power efficiency over GPU. |
Starke et al. (2012) [109] | Optimizing investment strategies; speedup > 17,000× compared to high-performance PC, FPGA 12–45 W vs. CPU 95 W and GPU 225 W. |
Jin et al. (2012) [110] | Optimization for stencil-based numerical procedures; 2× speedup. |
Kurek (2014) [111] | Automation optimization algorithms |
Czajkowski et al. (2012) [112] | OpenCL compilation frameworks; 1.2× speedup compared to handcrafted implementation. |
Krommydas et al. (2016) [114] | OpenCL for FPGA programming; 1.22× performance improvement. |
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O Mahony, A.; Hanzon, B.; Popovici, E. The Role of FPGAs in Modern Option Pricing Techniques: A Survey. Electronics 2024, 13, 3186. https://doi.org/10.3390/electronics13163186
O Mahony A, Hanzon B, Popovici E. The Role of FPGAs in Modern Option Pricing Techniques: A Survey. Electronics. 2024; 13(16):3186. https://doi.org/10.3390/electronics13163186
Chicago/Turabian StyleO Mahony, Aidan, Bernard Hanzon, and Emanuel Popovici. 2024. "The Role of FPGAs in Modern Option Pricing Techniques: A Survey" Electronics 13, no. 16: 3186. https://doi.org/10.3390/electronics13163186
APA StyleO Mahony, A., Hanzon, B., & Popovici, E. (2024). The Role of FPGAs in Modern Option Pricing Techniques: A Survey. Electronics, 13(16), 3186. https://doi.org/10.3390/electronics13163186