Investment Company utilize NAG Optimization Solvers to Calibrate Nonlinear Least Squares Problem

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Global Investment Company Exane turned to the Numerical Algorithms Group (NAG) to provide expert optimization solvers to calibrate parametric arbitrage-free volatility surfaces. Exane specialize in three finance areas: Cash Equities, Derivatives and Asset Management, and it was within the Equity Derivatives function that Exane benefitted from using NAG’s superior optimization solvers.

The Challenge

The Exane Quant Team for Equity Derivatives needed to quickly, efficiently and, on a continuous basis, solve a constrained nonlinear least squares optimization problem with approximately 50 parameters, 100 linear constraints and 100 nonlinear constraints.

The Solution

Having previously used the NAG Library routines in other applications, Exane team members selected NAG Library optimization routines and conducted an extensive test phase, including pitching them against other numerical libraries and several open source routines. During the testing phase NAG experts helped the Exane team achieve a proof of concept, overcoming the initial complexity challenges. At the end of the evaluation NAG was chosen to supply their solvers for a host of reasons including the extensive algorithmic coverage found in the NAG Library. The Library offers numerous algorithms for the same class of problems which means the user can choose exactly the right solver for the problem. Other benefits which made NAG the first choice were:

  • NAG’s highly skilled and experienced technical staff being on hand to help solve convergence issues.
  • The intelligent monitoring possibilities in the NAG Library, including verbose loggings which helped in development.
  • Full reproducibility and robustness across platforms (x32 and x64).

Speaking of the NAG Library, Christian Marzolin, Head of the Quant Team for Equity Derivatives at Exane said, “After more than one year in production, the NAG Library has given us full satisfaction in terms of performance and reliability. With the reactivity of the technical support team we have been able to progressively improve the quality of our results. I strongly recommend others to try it out.”