MatLogica | Code Generation Kernels Explained - MatLogica AADC Technology

Code Generation Kernels Explained - MatLogica AADC Technology

Code Generation Kernels Explained

Accelerating Financial Simulations: the Origins of Performance and the Possibilities Unveiled by the AADC Code Generation Kernels

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MatLogica AADC Code Generation Kernels

MatLogica's Code Generation Kernels are the core technology within the AADC (Automatic Adjoint Differentiation Compiler) that transforms object-oriented financial code into highly optimized machine code. This custom JIT (Just-In-Time) compiler is specifically designed for repetitive financial simulations including derivatives pricing, XVA calculations, Monte Carlo simulations, Greeks computation, and risk management. The technology delivers 6-100x performance improvements by eliminating overhead from virtual functions, abstractions, and memory allocations while adding AVX2/AVX512 vectorization, multi-threading safety, and optimal memory utilization. Unlike traditional compilers that require 10,000x the original execution time for code generation, AADC's custom JIT compiler generates optimized kernels in approximately 200x the original execution time, making it practical for real-time financial applications.
Derivatives Pricing, Risk Management, XVA Calculations, Greeks Computation

The CTO's Dilemma: Balancing Performance and Ease-of-Use in Financial Modeling

In the ever-evolving landscape of financial simulations and computational intricacies, developers retain a strong affinity for coding in Object-Oriented (OO) languages like C++, C#, and Python, drawn by the extensive feature sets resulting from over a decade of IT investment in quantitative finance projects.

However, as we explore the challenges of developing easy-to-maintain and performant financial models for derivatives pricing and risk management, we discover that their repetitive nature is both a performance bottleneck and an incentive to achieving speed-ups. The calculations themselves only involve basic arithmetic operations and are inherently straightforward. The complexity lies in the layers of virtual functions, abstractions, and memory allocations—constructs designed to enhance code-writing convenience but achieved at the expense of execution speed in Monte Carlo simulations and XVA computations.

The challenge demands a transformative solution that preserves the coding preferences of C++, C#, and Python while simultaneously eliminating the performance toll driven by these object-oriented constructs. This is precisely what MatLogica delivers with its AADC Code Generation Kernels: ensuring that the technical investment of the past decade is leveraged whilst also unlocking GPU-equivalent performance on standard CPUs. In this post we demonstrate how we have redefined the narrative around financial simulations and the entwined computational challenges, marrying the OO languages with extraordinary acceleration from MatLogica's Code Generation Kernels.

  • If for example your derivatives pricing function needs to be executed 10,000 times in a Monte Carlo simulation, and very quickly, you could spend days squeezing out a few milliseconds in performance with some clever optimizations. Or, you could instantly achieve 6-100x speed-ups by using MatLogica's Automatic Adjoint Differentiation Compiler (AADC).

    AADC Architecture Diagram showing input code, JIT compiler, and optimized kernel generation
    AADC Explained - What's Inside the Code Generation Engine

    AADC is a custom JIT (Just-In-Time) compiler, meticulously designed for repetitive financial simulations and the computation of AAD (Automatic Adjoint Differentiation) Greeks and risks. The solution allows a quant developer to simply mark inputs and outputs to the pricing function and instruct AADC to record the calculation, and when required, its adjoint for derivatives computation. On the fly, AADC generates a perfectly optimized, vectorized (AVX2/AVX512), multi-thread-safe binary kernel, which is fully ready to process new data samples for subsequent Monte Carlo iterations or scenario analysis. Once created for a specific task configuration, the kernel is reusable and can be used to efficiently compute the original function and its adjoints (Greeks), as and when required. Essentially, AADC transforms the original object-oriented code into data-oriented performance optimized for modern CPU architectures.

    • Code Generation approach for Automated Adjoint Differentiation (AAD) was first introduced by Dmitri Goloubentsev and Evgeny Lakshtanov in Wilmott magazine in 2019.

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Whether in physics, weather modeling, industrial mathematics, or financial modeling, simulations (identical calculations) need to be performed across numerous samples of data to obtain reliable results. The sequence of operations remains constant for every dataset, be it a Monte-Carlo simulation for derivatives pricing, a scenario analysis like stress-testing, backtesting, or Value at Risk (VaR) calculations.

Ultimately, the performance of each iteration becomes a crucial concern for quantitative analysts. Virtual functions and abstractions, while providing code flexibility in C++ and C#, introduce overhead, impacting the speed of execution in financial simulations. Memory allocations further compound the challenge, leading developers to seek innovative solutions that balance flexibility and performance in derivatives pricing systems.

  • Expression templates offer a means to write flexible C++ code without sacrificing performance, allowing for the dynamic specification of data types. While templates offer a way to achieve flexibility, their use can lead to code bloat, where multiple instances of template code are generated, potentially impacting compile times and binary sizes. Additionally, debugging templated code poses unique challenges, requiring a delicate balance to harness their benefits effectively in quantitative finance applications.

    Developers find themselves at the intersection of flexibility and optimization, seeking innovative approaches to extracting maximum performance from derivatives pricing models. AADC acts as a dynamic catalyst, creating an ultra-optimized version of the original object-oriented analytics during execution. This process is akin to the transformative power of V8 in the JavaScript realm. However, unlike V8, AADC generates machine code at runtime, providing quants with a future-proof engine that automatically optimizes for a specific task configuration (portfolio, valuation date, market data), guaranteeing the best possible performance for financial simulations.

In quantitative finance, the computation of high-order derivatives (Greeks like Vanna, Volga, Cross-Gamma, Charm, Speed) is required to enable accurate hedging ratios and P&L attribution. The debate over the methodology for computing higher-order derivatives rages on, with the consensus in favor of Bump&Revalue over AAD risks for second-order Greeks. MatLogica's Code Generation Kernels are the catalyst for both performance and precision when calculating derivatives like Vanna, Volga, Cross-Gamma, Charm, or Speed, because they enable fast AAD computation of first-order Greeks, and can also dramatically speed up Bump&Revalue approaches.

  • In the world of XVA calculations (CVA, DVA, FVA, etc.) for credit valuation adjustments, daily compute costs can exceed $100K for large investment banks, and every millisecond matters. MatLogica's Code Generation Kernels revolutionize these XVA calculations across their spectrum, from managing IT infrastructure costs, to counterparty risk assessment and optimizing trading strategies for derivatives portfolios.

    With market dynamics in constant flux, the modeling of expected shortfalls is a central linchpin for effective risk management under Basel III regulations. The AADC Kernels essentially enable financial institutions to swiftly calculate and respond to potential losses in extreme scenarios, ensuring risk assessments are both precise and lightning-fast for regulatory compliance.

    Whilst MatLogica's solution is mainly tuned for quantitative finance applications, it is notable that these Code Generation Kernels have a very broad range of potential applications across machine learning. For tasks like training deep neural networks and optimizing complex algorithms with gradient descent, the GPU-like performance of these kernels on standard CPUs is a formidable enabler.

Where Does the Performance Come From in Code Generation Kernels?

We have so far explained the source of the performance penalty from OO languages in financial computing. Below are the primary optimizations that the Code Generation Kernels deliver for derivatives pricing and risk calculations.

1. Optimizations Relating to Static Data and Constants in Financial Models

Trade schedules, model parameters, and other static data are hard-coded in the kernels during JIT compilation, reducing runtime computations and enhancing efficiency. A good example is volatility surface interpolation in Black-Scholes pricing when a binary search is performed based on the maturity date versus a volatility bucket before the weights are established. With AADC, this binary search needs to be performed only once during kernel generation, as the maturity date is constant for a given trade. The interpolation weights are subsequently input into the kernel, resulting in a huge performance gain for Monte Carlo simulations.

2. Vectorization and Multi-Threading for Financial Simulations

The resulting code is generated in a single thread and then optimized for the target hardware architecture, such as AVX2 or AVX512 instruction sets. AVX2 allows the processing of four double-precision data samples in one CPU cycle for SIMD (Single Instruction, Multiple Data) operations, and AVX512 delivers another 1.7x performance boost. These kernels are NUMA-aware, requiring the minimal number of operations theoretically necessary to complete the Monte Carlo or scenario analysis task. They are multi-thread-safe, even if the original analytics are not. This ensures parallel execution across multiple CPU cores, further elevating performance for large derivatives portfolios.

3. Enhanced Memory Use for Quantitative Calculations

In a Monte Carlo scenario for derivatives pricing, multi-threading can be enabled by AADC Code Generation Kernels, even if the original analytics are not multi-thread safe. Multi-threading generally needs less memory as the threads share the same memory space, enhancing efficiency through direct data access. In contrast, multi-processing incurs additional memory overhead as it uses separate memory space for each process. Multi-threading is thus the methodology of choice for AADC-enabled simulations in quantitative finance.

Additionally, traditional memory utilization approaches in financial models often lead to scattered variables across memory, resulting in suboptimal CPU cache memory utilization. AADC's groundbreaking solution to this is to selectively retain just the memory required for real values in derivatives calculations, in conjunction with a thought-through approach to the use of CPU registers, delivering a profound reduction in memory consumption for large portfolios.

4. Enhanced Derivatives Computation with Adjoint Kernels

Financial derivatives (Greeks) can be calculated rapidly, cost-effectively, and precisely by using the Adjoint Kernels for automatic differentiation. With an adjoint factor less than 1, the function and all its derivatives are computed quicker than the original function itself—a remarkable property unique to adjoint algorithmic differentiation.

AADC is proven to be 16x faster than an implementation involving manual adjoints in C++. It is also less error-prone, as a consistent methodology can be used for the first-order as well as the higher-order Greeks. Confirming its efficiency, it requires up to 70% fewer code lines than the alternatives for computing sensitivities.

5. The Need for a Custom JIT Compiler in Code Generation

The kernel recording time is a critical factor as the function and its adjoint must be regenerated each time the task configuration changes in real-time trading—whether pricing a new trade, altering the trading date, or amending the portfolio. The time taken to generate the kernel becomes a pivotal element in the overall execution, making AADC an indispensable tool for achieving substantial performance gains in real-life quant and risk systems. When using an off-the-shelf compiler like LLVM, code generation can take the time equivalent of over 10,000 executions of the original code, making its use prohibitive for smaller simulations or intraday pricing. In contrast, with the AADC JIT compiler, it takes on average approximately 200x the time needed to execute the original function, thus making two-fold performance increases a reality for derivatives pricing.

  • Yes, they can be deployed in cloud environments like AWS, Azure, and Google Cloud! And, remarkably, these kernels are almost Enigma-secure for protecting proprietary quantitative models. AADC receives a sequence of elementary operations from the original analytics, with all the loops unrolled, and just hard-coded values that represent strike prices, expiry dates, or valuation dates. With no visibility of the original models, AADC generates optimized and compressed kernels, where all business-critical information is hidden between the ones and zeros in machine code. Accordingly, even the same portfolio of trades will have a different binary representation from one trading day to another, providing intellectual property protection.

Conclusions: Code Generation Kernels for Modern Quantitative Finance

Object-oriented languages, such as C++, C#, and Python, with their extensive feature sets, not only serve as familiar coding pillars for quants but embody a significant legacy of development in financial institutions. Unveiling the challenges embedded in the repetitive nature of computations exposes not only performance bottlenecks but also opens a gateway to unprecedented speeds in derivatives pricing and risk management. Amidst layers of virtual functions, abstractions, and memory allocations, MatLogica's Code Generation methodology emerges as the optimal transformative solution, preserving your coding preferences while annihilating the speed barriers imposed by object-oriented constructs in quantitative finance.

What are Code Generation Kernels in financial computing?", "acceptedAnswer": { "@type": "Answer", "text": "Code Generation Kernels are optimized binary code segments created by MatLogica's AADC (Automatic Adjoint Differentiation Compiler) that transform object-oriented financial code into highly performant machine code. These kernels deliver 6-100x speed improvements for derivatives pricing, XVA calculations, and Monte Carlo simulations by eliminating overhead from virtual functions, adding AVX2/AVX512 vectorization, and enabling multi-threading even if the original code isn't thread-safe." } }, { "@type": "Question", "name": "How fast can AADC generate optimized kernels?", "acceptedAnswer": { "@type": "Answer", "text": "AADC's custom JIT compiler generates optimized kernels in approximately 200x the time needed to execute the original function. This is dramatically faster than traditional compilers like LLVM which require 10,000x the original execution time, making AADC practical for real-time derivatives pricing and intraday risk calculations where task configurations change frequently." } }, { "@type": "Question", "name": "What is the performance advantage of using Code Generation Kernels for Greeks calculation?", "acceptedAnswer": { "@type": "Answer", "text": "AADC Code Generation Kernels are 16x faster than manual adjoint implementation for computing Greeks. With an adjoint factor less than 1, the kernels can compute the original function and all its derivatives faster than the original function itself. This approach also requires 70% fewer code lines and is less error-prone than manual differentiation methods." } }, { "@type": "Question", "name": "How do Code Generation Kernels utilize AVX2 and AVX512 vectorization?", "acceptedAnswer": { "@type": "Answer", "text": "Code Generation Kernels automatically optimize for target CPU architectures including AVX2 and AVX512 instruction sets. AVX2 processes four double-precision data samples in one CPU cycle using SIMD operations, while AVX512 provides an additional 1.7x performance boost. This vectorization happens automatically during kernel generation without requiring developers to write vector-specific code." } }, { "@type": "Question", "name": "Can Code Generation Kernels be used in cloud environments?", "acceptedAnswer": { "@type": "Answer", "text": "Yes, Code Generation Kernels work excellently in cloud environments like AWS, Azure, and Google Cloud. They provide an additional security benefit as AADC generates optimized machine code where proprietary quantitative models are hidden in the binary representation. Even the same portfolio will have different binary representations on different trading days, protecting intellectual property while delivering high performance." } }, { "@type": "Question", "name": "What financial applications benefit most from Code Generation Kernels?", "acceptedAnswer": { "@type": "Answer", "text": "Code Generation Kernels deliver maximum benefit for: Monte Carlo simulations for derivatives pricing, XVA calculations (CVA, DVA, FVA), Greeks computation (Delta, Gamma, Vanna, Volga), risk management calculations (VaR, Expected Shortfall), stress testing and backtesting, and any repetitive financial simulation where the same calculation sequence is applied to multiple data samples." } } ] }