Integrating AADC into Existing Quantitative Finance Libraries

For well-established quant libraries (10+ years old, 10 million+ lines of code), performance optimization, numerical stability, and minimal refactoring effort are critical factors when considering any technology upgrade. Incorporating MatLogica AADC is a semi-automated process powered by a rich set of integration tools and methodologies to assist the initial integration and debugging processes for derivatives pricing and risk management systems.

An automated replacement of double with idouble (MatLogica's active type) is required as a first step, resulting in the same numerical and performance results as the original code. The next step is to identify the main Monte Carlo simulation loop, mark the inputs and outputs, and indicate the recording of the parameters for a single path to obtain the optimized kernel for use in subsequent iterations. While this process demands a nuanced understanding of the library's intricacies, the integration process is straightforward and its benefits are profound—transforming legacy financial code into a high-performance powerhouse with automatic differentiation capabilities.

Using MatLogica AADC for a New Quantitative Finance Project

By leveraging AADC's capabilities from the outset and architecting quant libraries from the ground up, developers are liberated from the time-consuming challenge of retrofitting an existing codebase. There are three main benefits to this greenfield approach: (1) clean up-front design optimized for performance, (2) minimal wasteful development efforts on manual optimizations, and (3) a guilt-free path to harnessing the full potential of modern hardware (AVX512, multi-threading). Starting afresh with AADC is therefore an opportunity to craft a derivatives pricing library with baked-in efficiency, enabling a seamless process for subsequent iterations and model additions.

Step 1: Drop-in Replacement with Active Type

As a first step, the MatLogica active type (idouble) must be introduced into the quantitative library. This active type enables MatLogica AADC to extract the valuation graph from your derivatives pricing or risk calculation functions.

This transformation can be performed by running a suite of automated integration scripts that safely and efficiently transform an existing codebase into a robust framework, ready to harness the benefits of MatLogica AADC for automatic differentiation and performance optimization.

Step 2: Record the Pricing Function for Kernel Generation

Next, we identify the function that is executed in Monte Carlo simulations and/or needs to have sensitivities (Greeks) computed using automatic adjoint differentiation. We instruct AADC to record the function and specify the inputs (market data, trade parameters) and outputs (valuations, cashflows) of the function.

Step 3: Execute the Optimized Function

Once we have the recording (optimized kernel), it is used instead of the original function to compute the derivatives valuation itself and its sensitivities (Greeks) where needed using ultra-fast automatic adjoint differentiation.

All done! Your quantitative finance code now runs 6-100x faster with full AAD capabilities.

Debugging Toolkit for Numerical Verification

In most cases, the results produced by AADC are identical to the numbers produced by the original derivatives pricing program. In some instances, numerical differences can be observed due to optimizations performed by AADC's JIT compiler. Consider an expression (a+b+c): mathematically, the order of operations doesn't matter, but in computer arithmetic, it may be impactful due to compounded floating-point rounding differences in financial calculations.

AADC comes with a comprehensive debugging toolkit that targets such corner cases. It will point exactly to the line of code where numerical differences arise, allowing confident resolution of any mismatches between original and optimized code.

Diagnostics Toolkit for Branch Handling

Also important is the correct handling of branches and if-statements in stochastic models. When the pricing function depends on stochastic conditions (e.g., barrier options, path-dependent payoffs), both branches must be recorded for accurate kernel generation. MatLogica's Diagnostics toolkit is designed for this purpose and will flag any part of the code where branches are not handled correctly, ensuring robust automatic differentiation across all code paths.