Library

The Xilinx ® Vitis™ Quantitative Finance library is a fundamental library aimed at providing a comprehensive FPGA acceleration library for quantitative finance. It is a free/open-source for a variety of real use cases, such as modeling, trading, evaluation, and risk management.

The Vitis Quantitative Finance library provides comprehensive tools from the bottom up for quantitative finance. It includes the lowest level modules and functions, the pre-defined middle kernel level, and the third level as pure software APIs working with pre-defined hardware overlays.

  • At the lowest level (L1), it offers useful statistical functions, numerical methods and linear algebra functions to support user implementation of advanced modeling, such as RNG, Monte Carlo, SVD, and specialist matrix solvers.
  • In the middle level (L2), pricing engines kernels are provided to evaluate common finance derivatives, such as equity products, interest-rate products, FX products, and credit products.
  • The software API level (L3) wraps the details of offloading acceleration with pre-built binary (overlay) and allow users to accelerate supported pricing tasks on Alveo cards without hardware development.

This article covers the two common option pricing engine (L2 level): European Option pricing engine and American Option pricing engine.

In Quantitative finance, option pricing is to calculate the perineum for purchasing for selling options.

In options trading, option pricing models provide the finance professional a fair value to adjust their trading strategies and portfolios.

The value of the options are calculated based on current value of the underlying asset, volatility of the underlying asset, dividends paid on the underlying asset, strike price of the option, time to expiration on the option and riskless interest rate.


Two common option pricing engines

European option and American Option are the most common kinds of options. European options may be exercised on expiry. American options may be exercised on any trading day on or before expiration.

European option pricing engine and American option pricing engine estimate the value of option based on Monte Carlo simulation method and Black-Scholes model.

As the below figure shows, the Monte Carlo simulation process is accelerated by multiple Monte Carlo model (MCM) units operating in dataflow, and each sub-module in MCM working in pipeline.

All sub-modules in MCM are connected by HLS stream.

The latency of pricing engines based on Monte Carlo simulation is:

Number of cycles = requiredSamples * timeSteps / MCM:

monte-carlo-simulation-process

Compared to the European option pricing option, the process of American option pricing is more complex and divided into three functions based on Longstaff-Schwartz algorithm.

  1. MCAmericanEnginePreSamples function generates a small set of samples for calibration.
  2. MCAmericanEngineCalibrate function uses the least-square method to calibrate the coefficient of regression model with samples from MCAmericanEnginePreSamples.
  3. MCAmericanEnginePricing function looks up the best exercise point by using the calibrated regression model.

Accelerators

Vitis Quantitative finance library provided optimized pricing engine APIs with template parameter for datatype, number of MCM in parallel, which affects the resource utilization, performance, and quality of the result.

Monte Carlo European pricing engine APIs:

template <typename DT = double, int UN = 10, bool Antithetic = false>

void MCEuropeanEngine (

    DT underlying,

    DT volatility,

    DT dividendYield,

    DT riskFreeRate,

    DT timeLength,

    DT strike,

    bool optionType,

    ap_uint <32>* seed,

    DT* output,

    DT requiredTolerance = 0.02,

    unsigned int requiredSamples = 1024,

    unsigned int timeSteps = 100,

    unsigned int maxSamples = 134217727

    )

Monte Carlo American pricing engine APIs:

template <typename DT = double, int UN = 2>

void MCAmericanEnginePreSamples (

    DT underlying,

    DT volatility,

    DT riskFreeRate,

    DT dividendYield,

    DT timeLength,

    DT strike,

    bool optionType,

    ap_uint <32>* seed,

    ap_uint <8*sizeof (DT)*UN>* priceOut,

    ap_uint <8*sizeof (DT)>* matOut,

    unsigned int calibSamples = 4096,

    unsigned int timeSteps = 100

)

template <typename DT = double, int UN = 2, int UN_STEP = 2>

void MCAmericanEngineCalibrate (

    DT timeLength,

    DT riskFreeRate,

    DT strike,

    bool optionType,

    ap_uint <8*sizeof (DT)*UN>* priceIn,

    ap_uint <8*sizeof (DT)>* matIn,

    ap_uint <8*sizeof (DT)*4>* coefOut,

    unsigned int calibSamples = 4096,

    unsigned int timeSteps = 100

    )

template <typename DT = double, int UN = 2>

void MCAmericanEnginePricing (

    DT underlying,

    DT volatility,

    DT dividendYield,

    DT riskFreeRate,

    DT timeLength,

    DT strike,

    bool optionType,

    ap_uint <32>* seed,

    ap_uint <8*sizeof (DT)*4>* coefIn,

    DT* output,

    DT requiredTolerance = 0.02,

    unsigned int requiredSamples = 4096,

    unsigned int timeSteps = 100,

    unsigned int maxSamples = 134217727

    )

The implementation of Monte Carlo American option pricing is to connect 3 functions through external memory (DDR/HBM). They are scheduled by XRT runtime to work in pipeline mode in host side, which is elaborated in the benchmark.

Monte Carlo American option

Results

Monte Carlo European Option Pricing
Workload size: 1 timestep, 47K paths
  Cold Run Warn Run
QuantLib 20.155ms 20.155ms
Vitis Quantitative Finance Library 0.053ms 0.01325ms
Acceleration 380 1521

Notes:

  1. Cold run: the end-to-end execution time of 1 option pricing run.
  2. Warm run: the mean of the end-to-end execution time of 100 options pricing run continuously.

The resource utilization is listed in the following tables. There is 4 PUs which could price 4 options in parallel to implement kernel-level parallel. Each PU has the same resource utilization.

  LUTs FFs BRAMs URAMs DSPs
1 PU 234072 376207 49 0 1594
4 PUs 936288 1504828 196 0 6376
total 1728000 3456000 2688 1280 12288
utilization ratio 54.18% 43.54% 7.29% 0 51.89%
  • American Option Pricing Engine

The performance is shown in the table below, our cold run has 176X, and warm run has 529X compared to baseline.

Monte Carlo American Option Pricing
Workload size: 100 timesteps, 24K paths
  Cold Run Warn Run
QuantLib 1038.105ms 1038.105ms
Vitis Quantitative Finance Library 5.87ms 1.96ms
Acceleration 176 529

The PU_0, PU_1 and PU_2 are working in pipeline mode. PU_2 and PU_3 are both the instance of MCAmericanEnginePricing and run in parallel to balance the throughput of pre-sample, calibration and pricing.

american-option-pricing-engine-fig1

The resource utilization is listed in the following tables.

  LUTs FFs BRAMs URAMs DSPs
PU_0 (pre-sample) 120756 185169 43 0 416
PU_1 (calibrate) 181793 267405 68 0 462
PU_2 (pricing) 251370 268839 71 0 911
PU_3 (pricing) 251370 268839 71 0 911
total of PUs 805289 990252 253 0 2700
total 1728000 3456000 2688 1280 12288
utilization ratio 46.6% 428.65% 9.41% 0 21.97%

Design Files

The source file for the option pricing benchmark can be downloaded from the Vitis Accelerated Libraries repository on GitHub: https://github.com/Xilinx/Vitis_Libraries/tree/master/quantitative_finance/L2/benchmarks


About Alvin Clark

About Alvin Clark

Alvin Clark is a Sr. Technical Marketing Engineer working on Software and AI Platforms at Xilinx, helping usher in the ACAP era of programmable devices.  Alvin has spent his career working and supporting countless FPGA and embedded designs in many varied fields ranging from Consumer to Medical to Aerospace & Defense.  He has a degree from the University of California, San Diego and is working on his graduate degree at the Georgia Institute of Technology.


About Zhenhong Guo

About Zhenhong Guo

Zhenhong Guo is a software development section manager working on foundational library development at Xilinx, providing an excellent FPGA acceleration solution to customers.  Zhenhong received a Masters degree in Microelectronics and Solid-State Electronics from Institute of Electronics, Chinese Academy of Sciences and has spent her career working on supporting quantitative finance and database libraries.