Functional Interpolation: Chartis STORM 50 on Tuesday, September 5th, 2023

**Title: Functional Interpolation and Neural Networks | Exploring the Power of Neural Networks for Approximating Complex Functions**


Welcome to our presentation on functional interpolation and neural networks! In this session, we will dive into the world of neural networks as function approximators and explore their applications in different contexts. Join us as Maxime Bergeron, Director of R&D at Riskfuel, provides insights into how neural networks can help us solve complex nonlinear problems efficiently and accurately.

Neural networks have revolutionized the field of machine learning by enabling us to approximate complex functions with ease. These powerful tools can be utilized in various domains, including finance, risk management, and research. By understanding their capabilities and potential, we can harness the true computational power of neural networks.

In this presentation, Maxime will take you on a journey through time, starting from ancient civilization’s struggle with quadratic equations to the modern challenges faced in finance. You will discover how the Babylonians used simple operations, such as square roots, to solve quadratic equations efficiently. Fast forward to today, and we will explore how neural networks can be used to solve complex finance problems, like multi-asset auto callables, by breaking them down into simple operations.

Maxime will also explain the mathematical foundation of neural networks, highlighting how a single hidden layer can approximate any function, making them incredibly versatile tools in solving a wide range of problems. Whether you are a finance professional looking for more efficient pricing methods or a researcher interested in the power of neural networks, this presentation is for you!

Join us and unlock the potential of neural networks in approximating functions and solving complex problems. Don’t miss out on this exciting opportunity to learn more about functional interpolation and neural networks. Watch now and visit [Chartis Research]( for more information on neural networks, risk management, and research.

*Keywords: neural networks, interpolation, risk management, risk tech, research*

*Source: [Chartis Research](*

**Video Transcript:**


We’re going to kind of switch gears for this next presentation, so we just went from the very wide world of broad-based language models, and I’m going to show you a little bit about the final frontier in the more zoomed-in world of real-time pricing with less general but more specialized neural networks. This here is a little preview of the cool things that you can do once you start playing around with those toys.

The theme for this particular style of neural networks is a very old and human problem. Let me introduce you to the family of problems, F, parameterized by that family F. Classically, humans encountered these problems one at a time, using slow methods to compute solutions. But what if we could break down that slow operation into a collection of simple operations, bifurcating time and accuracy? The Babylonians did just that around 2000 BC with quadratic equations. Instead of solving each quadratic problem individually, they built a stone table with known square roots, allowing them to look up solutions quickly and perform simple addition and division. This way, they separated time and accuracy, and you can learn from their approach when handling modern problems.

Fast forward to today, and we find ourselves struggling with financial problems that require solving partial differential equations efficiently. Traditional methods, like finite differences or Monte Carlo simulations, can be time-consuming and may not provide accurate results for complex financial products. So, can we find a way to represent the solutions operator of such problems efficiently? The answer lies in neural networks.

Neural networks excel in representing complex functions and have the potential to approximate any function with a single hidden layer. This means even highly discontinuous functions, like those found in multi-asset auto callables, can be tackled effectively. By utilizing neural networks, we can break down complex finance problems into simple operations, allowing for faster and more accurate solutions.

At Riskfuel, we have been exploring the power of neural networks in solving finance problems. Starting from simpler cases like Black-Shoals swaps, we have moved on to more complex scenarios like Bermuda swaptions and multi-asset auto callables, which involve thousands of input dimensions. Our aim is to provide efficient and accurate pricing solutions for these challenging financial instruments.

So, what is a deep neural net? In theory, you can approximate any function with a single hidden layer. While some backpropagation costs may arise, the flexibility of neural networks in handling complex functions, including their discontinuities and payoffs, makes them a valuable tool for solving a wide range of problems.

Join us on this journey to explore functional interpolation and neural networks. Discover how they can revolutionize your approach to solving complex problems efficiently and accurately. Watch the full presentation now and visit [Chartis Research]( for more information on neural networks, risk management, risk tech, and research.

*Source: [Original Video Transcript](*

Presentation: Functional interpolation and neural networks

Neural networks are function approximators that can define complex nonlinear functions. This session focused on the use of neural networks to approximate functions and contexts where this can be applied.

Maxime Bergeron, Director of R&D, Riskfuel

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#neuralnetworks #interpolation #riskmanagement #risk #risktech #research

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