In March 2018, financial investment AI startup KenshoTM 3 announced that it was being acquired for $550 million—the largest AI acquisition to date (Business Insider 08 March 2018). Not only was the size of the deal surprising but even more surprisingly it happened in the financial investment domain.
AI or catch phrases like „Deep Learning“ and „Neural Networks“ have been around in many industries and subject areas, from image recognition, speech recognition and natural language processing to targeted advertising, KYC4 and drug discovery where they are used to extract modellable features from large data sets.
The power of an Artificial Neural Network to build complex functional relationships is its ability to represent a general function of an n-dimensional real variable to a given degree of accuracy using one hidden layer and a sigmoid activation function (technically formulated as the Universal Approximation Theorem, cf. Cybenko ). The weights of the network are unknown and need to be calculated via a "learning" algorithm. For many applications though, more elaborate neural network configurations are used, including deep networks, recurrent networks and convolutional networks.
It is not surprising that most recently Neural Networks have also emerged as a tool in the world of mathematical finance, where they can play a significant role in replacing computational expensive algorithms while matching or even improving the accuracy of the results. Hence the aforementioned largest AI acquisition to date.
Developing efficient numerical algorithms for high dimensional partial differential equations (PDEs) for example has been one of the most challenging tasks in applied mathematics. As is well-known to physicists and mathematicians, the difficulty lies in the "curse of dimensionality", namely, as the dimensionality grows, the complexity of the algorithms grows exponentially.
As a software vendor with a reliable and stable customer base in Germany and Asia, we at pdv Financial Software GmbH developed our own version of a deep learning driven approach to price Bermudan Swaptions in the Libor Market Model (as proposed by Wang et al. ).
This algorithm is implemented in DECIDE5, pdv Financial Software GmbH's modern software platform, and confirms, that the Neural Network based approach is in fact a lot faster than Longstaff-Schwartz regression (the current gold standard for pricing Bermudan Swaptions) while achieving the same level of accuracy. As a next step, we see yet another new application of Artificial Neural Networks within DECIDE for the near future, namely in the SABR stochastic volatility model (introduced by Hagan et al. ).
The original approximation presented in the SABR model and its extensions are within constant use across a large number of institutions within financial markets, covering a range of asset classes. The underlying model can be fully represented using a two factor finite difference scheme, but this in itself presents a number of implementation challenges, in addition to being impractically non-performant. As such, there has been a reliance on increasingly sophisticated approximations. An alternative, general approach using Artificial Neural Networks (McGhee ) has shown to perform robustly to a high degree of accuracy in a fraction of the time taken for existing accurate schemes.
The next hot topic we are going to tackle with AI is managing model risk in XVA. With the increase of bilaterally cleared transactions and the resulting growth of the OTC market, XVA gains more and more attention. With CVA6, FVA7 and KVA8 already on the plate and MVA9 being on the horizon, the impact on XVA gradually becomes one of the most important decision criteria when weighing the counterparty to the trade.
Up to now XVA libraries are complicated calculation infrastructures with plenty of model risk involved. We aim to leverage artificial intelligence and machine learning in DECIDE to verify consistent algorithm behavior, for example by determining unstable model behavior or benchmarking via deep reinforcement learning.
With DECIDE being productive at our customers, we think it should not only provide the standard models for everyday use, like it already does, but also use of state of the art results of current research.
1 pdv Financial Software GmbH
2 Physicist & Financial Mathematician, Freelance Consultant
3 An S&P Global Company
4 Know Your Customer
5 DECIDE supports banks, brokers and stock exchanges as standard end-to-end software platform.
6 Credit Valuation Adjustment
7 Funding Valuation Adjustment
8 Capital Valuation Adjustment
9 Margin Valuation Adjustment