Genius Mathematics Consultants

How do you validate a neural network model? Neural networks are increasingly being fitted to slow derivative pricing, market risk and XVA models to create surrogate models with lightning fast execution times, among many other applications. So how would model validation work for a neural network model?

Two key components of model validation are 1) methodology review and 2) model testing on a discrete but hopefully fairly comprehensive set of test cases.

The methodology review of a surrogate neural network would have to be a review of the methodology of the original model it is intended to replicate. For NNs which are not surrogates, it should involve a review of the fitting data, the fitting algorithm and how the NN interpolates and extrapolates the data.

Regarding model testing, many point out that a neural network is an opaque “black box”, has potentially millions of parameters, and you could never test it on every possible set of input parameters. Even if it tests successfully on a set of test cases, it may still fail in between those cases. However, it’s worth noting that even conventional code is often proprietary and opaque to the model validator, and could also fail due to numerical convergence issues or code faults that surface only in rare cases. Admittedly, the large number of internal parameters and numerical fitting procedures of neural networks may make them particularly susceptible to this problem.

Even when validating a model expressed as an analytic formula, you are implicitly assuming that your are validating a smooth function which doesn’t “turn” too sharply, so that if the model is correct on a grid of test cases, it should also be within some tolerance for the “in between” cases.

A promising strategy for validating a neural network is to test it on a grid of input parameters, and then attempt to show that the in-between prices must be “near” the prices you have checked in some sense in order to obtain an upper bound on their errors as well. Something like a Lipschitz condition |p(x) – p(y)| < L |x-y| with global constant L would suffice. You might also impose structural constraints on the NN such as monotonicity, convexity, or bounded second derivatives etc during fitting process. These techniques give you control over how the NN behaves in between test cases, giving you confidence that the model will behave reasonably on all inputs. The extrapolation beyond the dataset also needs to handled carefully during both the fitting and the testing procedures. For example, an NN which replicates an option pricing model needs to behave satisfactorily on a far in the money or out of the money option.

For independent model validation consulting services, Contact Us anytime.

Think R&D is too costly or time consuming? You’re wrong! Your existing staff are busy with BAU, but without R&D you won’t be competitive in the future – and that’s where we come in!

Our PhD quantitative consultants augment your in-house team with part time or project-based research and development. We build quantitative tools and software for all industries from financial services to engineering.

AI-accelerated development has greatly increased what a small team of experts can achieve. So those sophisticated tools larger competitors are using? They can be yours much more affordably than you thought.

Drop us a message to start a discussion about your business, your industry, your competitors, and how we can work together to supercharge the sophistication of your business.

Derivatives and trading businesses are talking about replacing slow derivative pricing models with fast but equivalent neural networks.

Why? Once a neural network has been fitted to the outputs of a conventional derivative pricing model, it prices virtually instantaneously. This enables:

• Real-time pricing of computationally expensive derivatives
• Option trading strategies execute faster
• Real-time calculation of Greeks
• Massive scenario analysis with millions of scenarios
• Rapid market risk calculation including intraday VaR
• Impossibly slow XVA calculations become viable
• Dramatically faster volatility model calibration
• Superior portfolio optimization

Interested in partnering with PhD quant consultants to develop neural network pricing models for your business? Talk to Genius Mathematics Consultants today.

Industrial businesses generate huge volumes of data — vibration, current, temperature, pressure, images, process logs and more. The challenge is often not collecting data, but turning it into better decisions.

Fault Detection & Predictive Maintenance
Predict machine failures before they happen using variables such as vibration, current, temperature, noise and pressure. Machine learning can identify complex patterns associated with degradation and estimate failure risk — helping reduce catastrophic downtime and unnecessary maintenance.

Anomaly Detection
Detect unusual operating conditions automatically from historical data. Unlike traditional rule-based systems, anomaly detection can identify unexpected behaviour even when examples of previous failures are unavailable.

Sensor Fusion & Calibration
Many industrial systems rely on multiple sensors with different viewpoints, offsets, noise characteristics and nonlinear distortions. Machine learning can combine and calibrate these signals to produce more accurate and reliable measurements and conclusions.

Yield & Process Optimisation
Want to maximise throughput, yield or product quality? Machine learning can learn the relationship between process inputs and outcomes, helping identify operating conditions that improve performance and reduce waste.

Examples include:
• Manufacturing
• Energy systems
• Medical devices
• Scientific instrumentation
• Robotics and automation

Our PhD consultants develop advanced machine learning, optimisation and sensor data processing algorithms to solve real industrial problems.

Learn more about our sensor algorithm consulting services

The rapid advances in AI and automation has businesses and employees concerned about whether they’ll have a job in a few years. But one way to make sure your business is successful over the next decade is to be involved in facilitating the transition to more automated devices, systems and processes. At Genius Mathematics Consultants, we provide the mathematical and statistical algorithms to help you do that.

We build quantitative tools and algorithms across diverse industries like mining, medical devices, and finance, including:

• Automated AI model validation agents for banks and industry
• Production scheduling, logistics and cost optimisation platforms
• Medical signal and industrial sensor processing algorithms
• Automated quantitative decision systems for industry, financial trading and risk
• Independent validation and assurance of AI-generated quantitative work
• Any other mathematical or statistical algorithm you can think of!

AI accelerated development combined with oversight by human experts has made building sophisticated algorithms in-house fast and affordable – now is the time to supercharge the sophistication of your models, devices and tools to benefit your own customers.

We provide diverse automation and algorithm consulting services: if you can imagine it – we can build it!

Genius Mathematics Consultants – so much more than mathematics.

Not sure whether to hire a consultant/freelancer for your next quantitative finance or mathematical engineering project? Have you considered the extra costs of a permanent employee?

Recruitment costs
Onboarding costs
Superannuation
Training
Bonuses
Insurance
Relocation packages
Support costs like HR and management layers
Having to retain the employee during workload dips and dependency blockers
Redundancy payouts
Sick leave
Payroll tax
Paid holidays
Office space
IT equipment
Maternity leave
Long service leave

What if you could hire a quant say, 20% of full time, or as-needed on a project basis? And why limit yourself to only local expertise?

Talk to Genius Mathematics Consultants about a flexible, 21st century approach to meeting your quantitative finance and mathematical engineering resourcing requirements.

You might think that the most important attributes of a model validator would be things like:

• Mathematical competence, to ensure the technical correctness of the methodology and that numerical schemes converge
• Knowledge of business context to evaluate the appropriateness of the model, and compare against alternative models
• The ability to write clean, well-structured code
• Technical writing skills to prepare clear and comprehensive documentation

And these things are all important. But there’s another very important aspect of model validation that often gets overlooked: the ability to courageously and effective challenge management and stakeholders.

As risk professionals we’re supposed to speak up, push back and insist upon integrity. Yet doing so brings us into direct conflict with management politics, deadlines and incentives. However much financial services institutions talk about valuing a “speak up” culture, this fundamental misalignment of incentives is never going away.

And with AI use on the rise, we face new risks as people under pressure try to meet deadlines by using AI without checking the work carefully. That’s why at Genius Mathematics Consultants we validate both human generated models and AI generated models.

It’s so common to encounter managers and stakeholders trying to ignore model faults and obstruct their resolution. We’ve encountered:

• Managers using model oversight committees, an institution intended to improve model integrity, to instead block model fixes and changes for political reasons
• Managers trying to make technical decisions about models without involving quantitative or risk staff
• Managers referencing model documentation that doesn’t exist
• Vendors pretending that model faults don’t exist, in the hope of avoiding admitting to the client that their model is wrong (causing the client to continue unknowingly using an erroneous model)

This is why it’s so important that model validators can operate independently of management and stakeholders. Ideally, model validation capability would be external to the firm.

We’re proud of our external model validation service, which will not only ensure the highest quality of model validation, but operate with total independence of internal politics and with a high degree of integrity.

Are you looking to grow your model validation capability? We offer model validation consulting and advisory services, including validation of AI generated models, and developing automated validation systems.

Contact us today to discuss how our external consultants are the model risk solution that your business needs.

Do you have legacy code and spreadsheets for mathematical models that are:

• Difficult to understand, with little or no documentation
• Fragile or error-prone
• Slow or inefficient, limiting your ability to scale or run large analyses
• Built in outdated languages or complex spreadsheets that are hard to follow and maintain
• Dependent on key individuals, creating operational and knowledge risk

We can help you transform them into modern, robust mathematical software with clear documentation, and uplift the underlying mathematical methodology as we do so.

We can transform spreadsheets into production-quality code, or migrate code from one language to another (e.g. Excel/VBA/Matlab to Python or C#, or legacy systems into high-performance modern architectures). The result is software that is faster, more reliable, easier to maintain, and fully aligned with your current and future business needs.

In many cases, legacy systems not only suffer from technical issues but also embed outdated or suboptimal assumptions. As part of the rebuild process, we review and, where appropriate, enhance the underlying mathematical models—whether that involves improving numerical methods, correcting approximations, or extending functionality to support more realistic scenarios. This ensures that the new system is not just a cleaner implementation, but a genuine upgrade in capability and accuracy.

We also place a strong emphasis on testing, validation, and transparency. In fact, model validation consulting is one of our key services. Rebuilt systems are delivered with comprehensive test suites, clear audit trails, and documentation that allows your team to fully understand and confidently maintain the software going forward. The end result is a system that reduces operational risk, removes key-person dependencies, and provides a solid foundation for future development and scaling.

We also offer a wide range of other services relating to mathematical software development, engineering tools and financial modelling. Contact us today to learn more.

Monte Carlo simulation is used in investment management and portfolio optimization to model possible future outcomes for asset prices and portfolios. Instead of relying on a single forecast, it generates tens of thousands or millions of simulated paths based on asset data such as returns, volatility, and correlations, allowing managers to see the full distribution of potential results. This helps in assessing risk (such as drawdowns and tail losses), evaluating the robustness of investment strategies, and estimating the probability of achieving specific financial goals. It is particularly valuable for portfolios involving derivatives or dynamic strategies, where outcomes depend on the path of market movements rather than just the final price.

Why buy when you can build?

AI-accelerated development has significant reduced the cost and development time of investment management software. This means that now is an excellent time to reduce costs by bringing this functionality in-house, or to increase your modelling capabilities for a competitive advantage.

Commercial investment management platforms that incorporate Monte Carlo simulation are often expensive, inflexible, and not fully aligned with a firm’s specific needs, with ongoing licensing and customization costs adding up over time. In many cases, firms end up paying for generic functionality while still having to work around limitations in the system.

By contrast, building a tailored in-house solution can deliver both cost savings and a significantly better fit to your investment strategies and workflows. With the support of Genius Mathematics Consultants, your firm can design and implement high-performance Monte Carlo-based systems that are fully customized, transparent, and adaptable, without the long-term burden of vendor fees. This approach not only reduces costs but also provides greater control over models, assumptions, and future development.

What are the advantages of Monte Carlo simulation in investment management and portfolio optimization?

• A pension fund can model cashflows and asset returns jointly to estimate the probability of funding shortfalls under different contribution and allocation strategies, allowing it to choose a policy that minimises the risk of needing emergency capital injections.
• In asset allocation, Monte Carlo can be used to test how a portfolio performs under correlation breakdown scenarios—such as equities and bonds falling together—revealing vulnerabilities that standard mean-variance optimisation would miss.
• For structured products or illiquid investments, it can simulate path-dependent payoff profiles to understand how returns behave under stress, such as early drawdowns or prolonged low-return environments.
• A wealth manager can model different withdrawal strategies for clients—such as fixed percentage vs inflation-linked drawdowns—to quantify the probability of portfolio depletion under varying market conditions, enabling more robust retirement planning advice.
• A multi-asset fund can simulate liquidity stress scenarios, modelling how quickly positions can be unwound during market dislocations and estimating the impact on portfolio value, helping to avoid forced selling at distressed prices.
• A systematic trading strategy can be stress-tested by simulating execution delays, spread widening, and regime shifts to evaluate whether its apparent edge survives real-world trading frictions rather than idealised backtest assumptions.

Importantly, Monte Carlo simulations can be calibrated to

• Historical asset behaviour
• Historical asset behaviour during stressed scenarios such as the GFC
• Hypothetical scenarios

This allows asset managers to build up a complex picture of how their portfolio could behave under the widest range of possible and historical scenarios.

Let’s get the ball rolling

Keen to take advantage of AI efficiency increases to increase the sophistication of your investment modelling? Or keen to bring an existing vendor platform in-house to reduce costs and increase customization? Either way, we’ve got you covered.

Drop us a message today to get the ball rolling.

Are you looking to hire the services of a freelancer quant dev or quant researcher? Forget the extra admin work and fees of freelancer aggregation sites like Upwork, Toptal or Arc – work directly with a PhD-level quantitative expert. We help you with things like:

• Financial modelling in languages like python and C++/C#
• Automated/algorithmic trading systems including backtesting, execution logic and machine learning trading strategies. We focus on realistic modelling (slippage, latency, transaction costs) to avoid overstated performance.
• Risk systems including market risk and liquidity risk, including scenario analysis and stress testing. We help quantify risk in a way that supports clear decision-making.
• Development derivative pricing libraries for vanilla and exotic derivatives, including Monte Carlo methods and XVA
• Trading and modelling infrastructure for Crypto firms

Our approach combines modern AI-accelerated development with rigorous human expert validation:

• AI-assisted coding is used to accelerate development and reduce cost
• All models are then reviewed, tested, and validated by an experienced quantitative specialist

Engagements can be either project based, or take the form of a fractional retainer (e.g., 10 hours per week).

Contact us today to discuss how we can help solve your problem.