Black-Scholes shows how to use Random Number Generator (RNG) functionality available in Intel® oneAPI Math Kernel Library (oneMKL) to calculate the prices of options using the Black-Scholes formula for suitable randomly-generated portfolios.

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.

The Black-Scholes formula is widely used in financial markets as a basic prognostic tool. The ability to calculate it quickly for a large number of options has become a necessity and represents a classic problem in parallel computation.

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 SYCL_DEVICE_FILTER environment variable to cpu or gpu to select the device to use.

This article explains in detail how oneMKL functions speed up Black-Scholes computation of European options pricing: https://www.intel.com/content/www/us/en/docs/onemkl/cookbook/current/black-scholes-formula-european-options-pricing.html.

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.

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® oneAPI Toolkits.
• Configure the oneAPI environment with the extension Environment Configurator for Intel® oneAPI Toolkits.
• 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.

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*.

If running a sample in the Intel® DevCloud, remember that you must specify the compute node (CPU, GPU, FPGA) as well whether to run in batch or interactive mode. For more information see the Intel® oneAPI Base Toolkit Get Started Guide (https://devcloud.intel.com/oneapi/get-started/base-toolkit/).

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

You can remove all generated files with make clean.

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

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.

If everything is working correctly, the program will run the Black-scholes 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:

$ ./black_scholes_sycl

Double Precision Black&Scholes Option Pricing version 1.6 running on Intel(R) Xeon(R) Gold 6148 CPU @ 2.40GHz using DPC++, workgroup size 256, 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      : Apr 28 2023 05:34:33
Input Dataset   : 8388608
Pricing 16777216 Options in 512 iterations, 8589934592 Options in total.
Completed in    1.41111 seconds. GOptions per second:    6.08735
Time Elapsed =     1.41111 seconds
Creating the reference result...
L1 norm: 1.385136E-16
TEST PASSED

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

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.