Binomial Sample

Binomial shows how to use Random Number Generator (RNG) functionality available in Intel® oneAPI Math Kernel Library (oneMKL). It uses for european options pricing using binomial options pricing model for suitable randomly-generated portfolios.

Optimized for	Description
OS	Linux* Ubuntu* 18.04 Windows 10
Hardware	Skylake with Gen9 or newer
Software	Intel® oneAPI Math Kernel Library (oneMKL)
What you will learn	How to use the oneMKL random number generation functionality
Time to complete	15 minutes

For more information on oneMKL and complete documentation of all oneMKL routines, see https://www.intel.com/content/www/us/en/developer/tools/oneapi/onemkl-documentation.html.

Purpose

The binomial options pricing model is widely used in financial markets. It has a lot of computation after random numbers are generated.

The sample first generates a portfolio within given constraints using a uniform distribution and a Philox-type generator provided by the oneMKL RNG API.

This sample performs its computations on the default SYCL* device. You can set the ONEAPI_DEVICE_SELECTOR environment variable to "*:cpu" or "*:gpu" to select the device to use. To find more information about the variable follow the link: ONEAPI_DEVICE_SELECTOR.

Key Implementation Details

This sample illustrates how to create an RNG engine object (the source of pseudo-randomness), a distribution object (specifying the desired probability distribution), and finally generate the random numbers themselves.

In this sample, a Philox 4x32x10 generator is used. It is a lightweight counter-based RNG well-suited for parallel computing.

This sample has pretty heavy kernel. It means that the kernel contains a lot of computations.

Using Visual Studio Code* (Optional)

You can use Visual Studio Code (VS Code) extensions to set your environment, create launch configurations, and browse and download samples.

The basic steps to build and run a sample using VS Code include:

• Download a sample using the extension Code Sample Browser for Intel Software Developer Tools.
• Configure the oneAPI environment with the extension Environment Configurator for Intel Software Developer Tools.
• Open a Terminal in VS Code (Terminal>New Terminal).
• Run the sample in the VS Code terminal using the instructions below.
• (Linux only) Debug your GPU application with GDB for Intel® oneAPI toolkits using the Generate Launch Configurations extension.

To learn more about the extensions, see the Using Visual Studio Code with Intel® oneAPI Toolkits User Guide.

Building the Binomial Sample

Note: If you have not already done so, set up your CLI environment by sourcing the setvars script located in the root of your oneAPI installation.

Linux*:

• For system wide installations: . /opt/intel/oneapi/setvars.sh
• For private installations: . ~/intel/oneapi/setvars.sh
• For non-POSIX shells, like csh, use the following command: $ bash -c 'source <install-dir>/setvars.sh ; exec csh'

Windows*:

• C:\"Program Files (x86)"\Intel\oneAPI\setvars.bat
• For Windows PowerShell*, use the following command: cmd.exe "/K" '"C:\Program Files (x86)\Intel\oneAPI\setvars.bat" && powershell'

For more information on configuring environment variables, see Use the setvars Script with Linux* or MacOS* or Use the setvars Script with Windows*.

On a Linux* System

Run make to build the sample. Then run the sample calling generated execution file.

You can remove all generated files with make clean.

On a Windows* System

Run nmake to build and run the sample programs. nmake clean removes temporary files.

Build a sample using Random Number Generation on Host

To use the RNG on host use init_on_host=1, e.g.

make init_on_host=1

for Linux* system or

nmake init_on_host=1

for Windows* System.

Running the Binomial Sample

If everything is working correctly, the program will run the Binomial simulation. After the simulation, results will be checked against the known true values given by the Black-Scholes formula, and the absolute error is output.

Example of output:

$ ./binomial_sycl

Double Precision Binomial Option Pricing version 1.8 running on Intel(R) Xeon(R) Gold 6148 CPU @ 2.40GHz using DPC++, workgroup size 128, sub-group size 32.
Compiler Version: Intel(R) oneAPI DPC++/C++ Compiler 2023.1.0 (2023.1.0.20230320), LLVM 16.0 based.
Driver Version  : 2023.15.3.0.20_160000
Build Time      : May  3 2023 03:51:58
Input Dataset   : 8388608
Pricing 8388608 Options with time step of 2048.
Cold iteration.
Completed in  379.85246 seconds. Options per second: 22083.85865
Warm iteration.
Completed in  378.85559 seconds. Options per second: 22141.96683
Time Elapsed =   378.85559 seconds
Creating the reference result...
L1 norm: 2.645901E-06
TEST PASSED

Troubleshooting

If an error occurs, troubleshoot the problem using the Diagnostics Utility for Intel® oneAPI Toolkits. Learn more.

License

Code samples are licensed under the MIT license. See License.txt for details.

Third party program Licenses can be found here: third-party-programs.txt.