Optimization algorithms are commonly used in the financial industry with examples including Markowitz portfolio optimization, Asset-Liability management, credit-risk management, volatility surface estimation etc. Many optimization problems involve nonlinear objective functions and constraints. These problems can be computationally expensive, especially with numerically estimated gradients. We have seen many cases where optimizations were sped up by incorporating pre-computed analytical derivatives.
In this article, we illustrate how optimization problems can be sped up using this approach with MATLAB and Symbolic Math Toolbox.
Note: This article was co-authored by Sri Krishnamurthy when he was employed at MathWorks.