# Vitis Quantitative Finance Library¶

The Vitis Quantitative Finance Library is a Vitis Library aimed at providing a comprehensive FPGA acceleration library for quantitative finance. It is an open-sourced library that can be used in a variety of financial applications, such as modeling, trading, evaluation and risk management.

The Vitis Quantitative Finance Library provides extensive APIs at three levels of abstraction:

- L1, the basic functions heavily used in higher level implementations. It includes statistical functions such as Random Number Generation (RNG), numerical methods, e.g., Monte Carlo Simulation, and linear algebra functions such as Singular Value Decomposition (SVD), and tridiagonal and pentadiagonal matrix solvers.
- L2, the APIs provided at the level of pricing engines. Various pricing engines are provided to evaluate different financial derivatives, including equity products, interest-rate products, foreign exchange (FX) products, and credit products. At this level, each pricing engine API can be seen as a kernel. The customers may write their own CPU code to call different pricing engines under the framework of OpenCL.
- L3, the software level APIs. APIs of this level hide the details of data transfer, kernel related resources configuration, and task scheduling in OpenCL. Software application programmers may quickly use L3 high-level APIs to run various pricing options without touching the dependency of OpenCL tasks and hardware configurations.

## Library Contents¶

Library Class | Description | Layer |
---|---|---|

MT19937 | Random number generator | L1 |

MT2203 | Random number generator | L1 |

MT19937IcnRng | Random number generator | L1 |

MT2203IcnRng | Random number generator | L1 |

MT19937BoxMullerNormalRng | Produces a normal distribution from a uniform one | L1 |

MultiVariateNormalRng | Random number generator | L1 |

SobolRsg | Quasi-random number generator | L1 |

SobolRsg1D | Quasi-random number generator | L1 |

BrownianBridge | Brownian bridge transformation using inverse simulation | L1 |

TrinomialTree | Lattice-based trinomial tree structure | L1 |

TreeLattice | Generalized structure compatible with different models and instruments | L1 |

Fdm1dMesher | Discretization for finite difference method | L1 |

OrnsteinUhlenbeckProcess | A simple stochastic process | L1 |

StochasticProcess1D | 1-dimentional stochastic process derived by RNG | L1 |

HWModel | Hull-White model for tree engine | L1 |

G2Model | Two-additive-factor gaussian model for tree engine | L1 |

ECIRModel | Extended Cox-Ingersoll- Ross model | L1 |

CIRModel | Cox-Ingersoll-Ross model for tree engine | L1 |

VModel | Vasicek model for tree engine | L1 |

HestonModel | Heston process | L1 |

BKModel | Black-Karasinski model for tree engine | L1 |

BSModel | Black-Scholes process | L1 |

XoShiRo128PlusPlus | XoShiRo128PlusPlus | L1 |

XoShiRo128Plus | XoShiRo128Plus | L1 |

XoShiRo128StarStar | XoShiRo128StarStar | L1 |

BicubicSplineInterpolation | Bicubic Spline Interpolation | L1 |

CubicInterpolation | Cubic Interpolation | L1 |

BinomialDistribution | Binomial Distribution | L1 |

CPICapFloorEngine | Pricing Consumer price index (CPI) using cap/floor methods | L2 |

DiscountingBondEngine | Engine used to price discounting bond | L2 |

InflationCapFloorEngine | Pricing inflation using cap/floor methods | L2 |

FdHullWhiteEngine | Bermudan swaption pricing engine using finite- difference methods based on Hull-White model | L2 |

FdG2SwaptionEngine | Bermudan swaption pricing engine using finite- difference methods based on two-additive-factor gaussian model | L2 |

DeviceManager | Used to enumerate available Xilinx devices | L3 |

Device | A class representing an individual accelerator card | L3 |

Trace | Used to control debug trace output | L3 |

Library Function | Description | Layer |
---|---|---|

svd | Singular Value Decomposition using the Jacobi method | L1 |

mcSimulation | Monte-Carlo Framework implementation | L1 |

pentadiagCr | Solver for pentadiagonal systems of equations using PCR | L1 |

boxMullerTransform | Box-Muller transform from uniform random number to normal random number | L1 |

inverseCumulativeNormalPPND7 | Inverse Cumulative transform from random number to normal random number | L1 |

inverseCumulativeNormalAcklam | Inverse CumulativeNormal using Acklam’s approximation to transform uniform random number to normal random number | L1 |

trsvCore | Solver for tridiagonal systems of equations using PCR | L1 |

PCA | Principal Component Analysis library implementation | L1 |

bernoulliPMF | Probability mass function for bernoulli distribution | L1 |

bernoulliCDF | Cumulative distribution function for bernoulli distribution | L1 |

covCoreMatrix | Calculate the covariance of the input matrix | L1 |

covCoreStrm | Calculate the covariance of the input matrix | L1 |

covReHardThreshold | Hard-thresholding Covariance Regularization | L1 |

covReSoftThreshold | Soft-thresholding Covariance Regularization | L1 |

covReBand | Banding Covariance Regularization | L1 |

covReTaper | Tapering Covariance Regularization | L1 |

gammaCDF | Cumulative distribution function for gamma distribution | L1 |

linearImpl | 1D linear interpolation | L1 |

normalPDF | Probability density function for normal distribution | L1 |

normalCDF | Cumulative distribution function for normal distribution | L1 |

normalICDF | Inverse cumulative distribution function for normal distribution | L1 |

logNormalPDF | Probability density function for log-normal distribution | L1 |

logNormalCDF | Cumulative distribution function for log-normal distribution | L1 |

logNormalICDF | Inverse cumulative distribution function for log-normal distribution | L1 |

poissonPMF | Probability mass function for poisson distribution | L1 |

poissonCDF | Cumulative distribution function for poisson distribution | L1 |

poissonICDF | Inverse cumulative distribution function for poisson distribution | L1 |

binomialTreeEngine | Binomial tree engine using CRR | L2 |

cfBSMEngine | Single option price plus associated Greeks | L2 |

FdDouglas | Top level callable function to perform the Douglas ADI method | L2 |

hcfEngine | Engine for Hestion Closed Form Solution | L2 |

M76Engine | Engine for the Merton Jump Diffusion Model | L2 |

MCEuropeanEngine | Monte-Carlo simulation of European-style options | L2 |

MCEuropeanPriBypassEngine | Path pricer bypass variant | L2 |

MCEuropeanHestonEngine | Monte-Carlo simulation of European-style options using Heston model | L2 |

MCmultiAssetEuropeanHestonEngine | Monte-Carlo simulation of European-style options for multiple underlying asset | L2 |

MCAmericanEnginePreSamples | PreSample kernel: this kernel samples some amount of path and store them to external memory | L2 |

MCAmericanEngineCalibrate | Calibrate kernel: this kernel reads the sample price data from external memory and use them to calculate the coefficient | L2 |

MCAmericanEnginePricing | Pricing kernel | L2 |

MCAmericanEngine | Calibration process and pricing process all in one kernel | L2 |

MCAsianGeometricAPEngine | Asian Arithmetic Average Price Engine using Monte Carlo Method Based on Black-Scholes Model : geometric average version | L2 |

MCAsianArithmeticAPEngine | arithmetic average version | L2 |

MCAsianArithmeticASEngine | Asian Arithmetic Average Strike Engine using Monte Carlo Method Based on Black-Scholes Model : arithmetic average version | L2 |

MCBarrierNoBiasEngine | Barrier Option Pricing Engine using Monte Carlo Simulation | L2 |

MCBarrierEngine | Barrier Option Pricing Engine using Monte Carlo Simulation | L2 |

MCCliquetEngine | Cliquet Option Pricing Engine using Monte Carlo Simulation | L2 |

MCDigitalEngine | Digital Option Pricing Engine using Monte Carlo Simulation | L2 |

MCEuropeanHestonGreeksEngine | European Option Greeks Calculating Engine using Monte Carlo Method based on Heston valuation model | L2 |

MCHullWhiteCapFloorEngine | Cap/Floor Pricing Engine using Monte Carlo Simulation | L2 |

McmcCore | Uses multiple Markov Chains to allow drawing samples from multi mode target distribution functions | L2 |

treeSwaptionEngine | Tree swaption pricing engine using trinomial tree based on 1D lattice method | L2 |

treeSwapEngine | Tree swap pricing engine using trinomial tree based on 1D lattice method | L2 |

treeCapFloprEngine | Tree cap/floor engine using trinomial tree based on 1D lattice method | L2 |

treeCallableEngine | Tree callable fixed rate bond pricing engine using trinomial tree based on 1D lattice method | L2 |

hjmEngine | Full implementation of Heath-Jarrow-Morton framework Pricing Engine with Monte Carlo | L2 |

hjmMcEngine | Monte Carlo only implementation of Heath-Jarrow-Morton framework Pricing Engine | L2 |

hjmPcaEngine | PCA only implementation of Heath-Jarrow-Morton framework | L2 |

lmmEngine | LIBOR Market Model (BGM) framework implementation. | L2 |

## Shell Environment¶

Setup the build environment using the Vitis and XRT scripts, and set the `PLATFORM_REPO_PATHS`

to installation folder of platform files.

source <vitis_path>/Vitis/2021.1/settings64.sh source <xrt_path>/xrt/setup.sh export PLATFORM_REPO_PATHS=<platform_path>/platforms

## Design Flows¶

Recommended design flows are categorized by the target level:

- L1
- L2
- L3

The common tool and library prerequisites that apply across all design flows are documented in the requirements section above.

### L1¶

L1 provides the low-level primitives used to build kernels.

The recommend flow to evaluate and test L1 components is described as follows using the Vitis HLS tool. A top level C/C++ testbench (typically main.cpp or tb.cpp) prepares the input data, passes this to the design under test (typically dut.cpp which makes the L1 level library calls) then performs any output data post processing and validation checks.

A Makefile is used to drive this flow with available steps including CSIM (high level simulation), CSYNTH (high level synthesis to RTL), COSIM (cosimulation between software testbench and generated RTL), VIVADO_SYN (synthesis by Vivado), and VIVADO_IMPL (implementation by Vivado). The flow is launched from the shell by calling make with variables set as in the example below:

# entering specific unit test project cd L1/tests/specific_algorithm/ # Only run C++ simulation on U250 make run CSIM=1 CSYNTH=0 COSIM=0 VIVADO_SYN=0 VIVADO_IMPL=0 DEVICE=u250_xdma_201830_1

As well as verifying functional correctness, the reports generated from this flow give an indication of logic utilization, timing performance, latency and throughput. The output files of interest can be located at the location examples as below where the file names are correlated with the source code. i.e. the callable functions within the design under test.:

```
Simulation Log: <library_root>/L1/tests/bk_model/prj/solution1/csim/report/dut_csim.log
Synthesis Report: <library_root>/L1/tests/bk_model/prj/solution1/syn/report/dut_csynth.rpt
```

### L2¶

L2 provides the pricing engine APIs presented as kernels.

The available flow for L2 based around the Vitis tool facilitates the generation and packaging of pricing engine kernels along with the required host application for configuration and control. In addition to supporting FPGA platform targets, emulation options are available for preliminary investigations or where dedicated access to a hardware platform may not be available. Two emulation options are available, software emulation performs a high level simulation of the pricing engine while hardware emulation performs a cycle-accurate simulation of the generated RTL for the kernel. This flow is makefile driven from the console where the target is selected as a command line parameter as in the examples below:

cd L2/tests/GarmanKohlhagenEngine # build and run one of the following using U250 platform # * software emulation make run TARGET=sw_emu DEVICE=u250_xdma_201830_1 # * hardware emulation make run TARGET=hw_emu DEVICE=u250_xdma_201830_1 # * actual deployment on physical platform make run TARET=hw DEVICE=u250_xdma_201830_1 # delete all xclbin and host binary make cleanall

The outputs of this flow are packaged kernel binaries (xclbin files) that can be downloaded to the FPGA platform and host executables to configure and co-ordinate data transfers. The output files of interest can be located at the locations examples as below where the file names are correlated with the source code.:

```
Host Executable: L2/tests/GarmanKohlhagenEngine/bin_#DEVICE/gk_test.exe
Kernel Packaged Binary: L2/tests/GarmanKohlhagenEngine/xclbin_#DEVICE_#TARGET/gk_kernel.xclbin #ARGS
```

This flow can be used to verify functional correctness in hardware and enable real world performance to be measured.

### L3¶

L3 provides the high level software APIs to deploy and run pricing engine kernels whilst abstracting the low level details of data transfer, kernel related resources configuration, and task scheduling.

The flow for L3 is the only one where access to an FPGA platform is required.

A prerequisite of this flow is that the packaged pricing engine kernel binaries (xclbin files) for the target FPGA platform target have been made available for download or have been custom built using the L2 flow described above.

This flow is makefile driven from the console to initially generate a shared object (`L3/src/output/libxilinxfintech.so`

).

cd L3/src source env.sh make

The shared object file is written to the example location as shown below:

```
Library: L3/src/output/libxilinxfintech.so
```

User applications can subsequently be built against this library as in the example provided

cd L3/examples/MonteCarlo make all cd output # manual step to copy or create symlinks to xclbin files in current directory ./mc_example