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Revolutionizing Finance: How Automatic Differentiation is Cutting Down Computation Times by Over 600x! Does Automatic Differentiation Answer The Recent Explosion of Computation Needs In Finance?

Revolutionizing Finance: How Automatic Differentiation is Cutting Down Computation Times by Over 600x! Does Automatic Differentiation Answer The Recent Explosion of Computation Needs In Finance?

Technology

How automatic differentiation relates to symbolic differentiation.

“Mini-symposium on Automatic Differentiation and its Applications in the Financial Industry”

Authors: Sébastien Geeraert, Charles-Albert Lehalle, Barak Pearlmutter, Olivier Pironneau (LJLL), Adil Reghai

“Mini-symposium on Automatic Differentiation and its Applications in the Financial Industry” by Geeraert et al. delves into the significance and practical applications of Automatic Differentiation (AD) within the financial sector. The authors provide a comprehensive overview of AD as an essential tool for enhancing the accuracy of numerical computations of derivatives, particularly in the context of financial market participants who need to compute sensitivities to understand variations in their balance sheets.

Overview and Importance

Automatic Differentiation has long been recognized in applied mathematics for its ability to improve derivative computations’ accuracy compared to finite difference methods. This technique involves applying the chain rule mechanically through software solutions, providing exact derivative values. However, AD comes with a cost in terms of memory and CPU consumption, making it a resource-intensive approach.

An image demonstrating the computational graph for automatic differentiation of the function 𝑓(𝑥)=𝑥2+3𝑥+5f(x)=x2+3x+5. The graph shows the flow of operations and the reverse mode differentiation, illustrating the calculation of derivatives.

For financial institutions, including banks, insurance companies, and financial intermediaries, computing derivatives is crucial for assessing exposure sensitivities to market movements. This necessity has become even more pronounced following the 2008 financial crisis, with regulatory requirements mandating comprehensive exposure calculations across various market scenarios. The paper argues that AD offers a partial solution to the increasing computational demands in the financial industry.

Methodology and Findings

The authors explore the application of Adjoint Algorithmic Differentiation (AAD) within financial markets. They highlight that while AAD provides a significant computational advantage, it is not sufficient on its own. Financial sensitivities often involve complex functions and require integration with Monte Carlo simulations, necessitating specialized tools and theoretical results.

The paper presents a comparison between traditional Monte Carlo (MC-MC) methods and the proposed AAD approach. The results demonstrate a substantial reduction in computing time when using AAD. For instance, in valuing the Credit Valuation Adjustment (CVA) for a double barrier option, the AAD method significantly outperforms the standard approach:

  • CVA with MC-MC: 10,000 paths for prices and 10,000 paths for CVA, requiring approximately 5 hours.
  • CVA with AAD: Step 1 with 1,000,000 paths and Step 2 with 10,000 paths, taking only 29 seconds.

This comparison, conducted on an Intel Core i7-2600 CPU with 16 GB of RAM, highlights a speedup factor of over 620 times with the AAD method. Additionally, the AAD approach directly yields the surface of hedging sensitivities without requiring further simulations, unlike the MC-MC framework.

Practical Implications

The research underscores the significant impact of AAD on the calculation and management of CVA for banks. By enhancing computational efficiency and enabling the simultaneous acquisition of sensitivities to all input parameters, AAD becomes a critical tool for risk management and regulatory compliance. The ability to obtain these sensitivities efficiently is vital for financial institutions managing extensive derivatives portfolios.

Read the full paper:

[1703.02311] Mini-symposium on automatic differentiation and its applications in the financial industry (arxiv.org)

Revolutionizing Finance: How Automatic Differentiation is Cutting Down Computation Times by Over 600x! Does Automatic Differentiation Answer The Recent Explosion of Computation Needs In Finance?

Cornell Financial Engineering Manhattan 2024 Future of Finance Conference