Modeling Implied Volatility Surfaces using 2D Penalized B-Splines: A Numerical Analysis
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| Natura: | Recurso digital |
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2025
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| _version_ | 1866902257650368512 |
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| author | Conway-Burt, Sebastian |
| author_facet | Conway-Burt, Sebastian |
| contents | <p>This report investigates numerical methods for constructing implied volatility surfaces (IVS) from financial option data, with a focus on stability, convergence, and error analysis. Developed as a capstone for the Computational Mathematics Certificate at the University of Colorado Boulder, the study applies Newton-Raphson root-finding, natural cubic spline interpolation, and two-dimensional penalized B-splines solved with LSQR. The work explores the trade-off between accuracy and smoothness in volatility surface modeling and demonstrates that minimally penalized fits (λ ≈ 0.0001–1.0) achieve strong performance while avoiding oscillations. The findings contribute to applied numerical analysis in finance and illustrate practical applications of computational mathematics techniques.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_16930181 |
| institution | Zenodo |
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| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Modeling Implied Volatility Surfaces using 2D Penalized B-Splines: A Numerical Analysis Conway-Burt, Sebastian Implied volatility Volatility surface Penalized B-splines LSQR algorithm Numerical analysis Computational finance Option pricing <p>This report investigates numerical methods for constructing implied volatility surfaces (IVS) from financial option data, with a focus on stability, convergence, and error analysis. Developed as a capstone for the Computational Mathematics Certificate at the University of Colorado Boulder, the study applies Newton-Raphson root-finding, natural cubic spline interpolation, and two-dimensional penalized B-splines solved with LSQR. The work explores the trade-off between accuracy and smoothness in volatility surface modeling and demonstrates that minimally penalized fits (λ ≈ 0.0001–1.0) achieve strong performance while avoiding oscillations. The findings contribute to applied numerical analysis in finance and illustrate practical applications of computational mathematics techniques.</p> |
| title | Modeling Implied Volatility Surfaces using 2D Penalized B-Splines: A Numerical Analysis |
| topic | Implied volatility Volatility surface Penalized B-splines LSQR algorithm Numerical analysis Computational finance Option pricing |
| url | https://doi.org/10.5281/zenodo.16930181 |