The authors implemented this technique within the systems of a tier-one bank to approximate Front Office pricing functions with the aim of reducing the substantial computational burden associated with capital calculation as specified by FRTB IMA. The results show that in all cases, the computational burden reductions obtained were more than 90%, while maintaining high degrees of accuracy. This was achieved due to the mathematical properties enjoyed by Chebyshev Tensors. The authors' approach involves using orthogonal polynomials to represent complex functions in a compact form, which can then be efficiently evaluated using tensor-product algorithms. By leveraging these techniques, they were able to significantly reduce computation times while still achieving accurate results. Overall, this paper provides an innovative solution to address one of the major challenges faced by financial institutions when implementing FRTB IMA regulations. The proposed Orthogonal Chebyshev Sliding Technique has demonstrated its effectiveness in reducing computational burdens without sacrificing accuracy, making it a valuable tool for banks and other financial institutions seeking to optimize their capital calculations.
A bank used a special way to make their computer work faster when calculating money stuff. They used something called Chebyshev Tensors which are like special math tools that can help solve problems in a simpler way. They also used something called Tensor-product algorithms which helped them do the math even faster. With this new technique, they were able to save a lot of time and still be very accurate. This is good for banks who want to save time and do their work better.
Definitions
- Computational burden: The amount of work or effort needed to complete a task using a computer.
- FRTB IMA: A set of rules and regulations related to how banks calculate their capital requirements.
- Chebyshev Tensors: A mathematical tool that helps simplify complex functions.
- Orthogonal polynomials: A type of mathematical function that has certain properties that make it useful for solving problems.
- Tensor-product algorithms: A method for solving mathematical equations by breaking them down into smaller parts.
Reducing Computational Burden with Orthogonal Chebyshev Sliding Technique
Financial institutions are facing a major challenge when implementing the Fundamental Review of the Trading Book (FRTB) Internal Model Approach (IMA). This regulation requires banks to calculate their capital requirements, which can be a computationally intensive process. To address this issue, researchers have developed an innovative solution known as the Orthogonal Chebyshev Sliding Technique (OCST). In this article, we will discuss how OCST works and explore its effectiveness in reducing computational burden while maintaining high accuracy.
What is FRTB IMA?
The Fundamental Review of the Trading Book (FRTB) Internal Model Approach (IMA) is a set of regulations introduced by the Basel Committee on Banking Supervision in 2017. These regulations require financial institutions to calculate their capital requirements based on market risk factors such as volatility and correlation. The calculations involved can be extremely complex and time-consuming, making it difficult for banks to comply with these regulations without incurring significant costs.
What is OCST?
Orthogonal Chebyshev Sliding Technique (OCST) is an innovative approach developed by researchers to reduce computational burden associated with FRTB IMA calculations. It involves using orthogonal polynomials to represent complex functions in a compact form that can then be efficiently evaluated using tensor-product algorithms. By leveraging these techniques, they were able to significantly reduce computation times while still achieving accurate results.
How Does OCST Work?
At its core, OCST works by approximating Front Office pricing functions within systems of tier-one banks using mathematical properties enjoyed by Chebyshev Tensors. This allows for efficient evaluation of complex functions through tensor-product algorithms instead of traditional methods which require more computing power and time. The authors implemented this technique within their systems and found that it was able to reduce computational burdens by more than 90%, while still maintaining high degrees of accuracy in all cases tested.
Conclusion:
Overall, this paper provides an innovative solution to address one of the major challenges faced by financial institutions when implementing FRTB IMA regulations – namely reducing computational burden without sacrificing accuracy when calculating capital requirements under these new rules. The proposed Orthogonal Chebyshev Sliding Technique has demonstrated its effectiveness in doing so, making it a valuable tool for banks and other financial institutions seeking to optimize their capital calculations under FRTB IMA regulations
In this paper we introduce a new technique based on high-dimensional Chebyshev Tensors that we call \emph{Orthogonal Chebyshev Sliding Technique}. We implemented this technique inside the systems of a tier-one bank, and used it to approximate Front Office pricing functions in order to reduce the substantial computational burden associated with the capital calculation as specified by FRTB IMA. In all cases, the computational burden reductions obtained were of more than $90\%$, while keeping high degrees of accuracy, the latter obtained as a result of the mathematical properties enjoyed by Chebyshev Tensors.
