Zhe Wang, Ameir Shaa, Nicolas Privault, Claude Guet
arXiv 9 Dec 2021 · Finance — Computational · publishedThe Journal of Computational Finance (2025)
arXiv:2201.07880 · PDF · DOI · OpenAlex · Extracted main text
We present an algorithm for the calibration of local volatility from market option prices through deep self-consistent learning, by approximating both market option prices and local volatility using deep neural networks. Our method uses the initial-boundary value problem of the underlying Dupire's partial differential equation solved by the parameterized option prices to bring corrections to the parameterization in a self-consistent way. By exploiting the differentiability of neural networks, we can evaluate Dupire's equation locally at each strike-maturity pair; while by exploiting their continuity, we sample strike-maturity pairs uniformly from a given domain, going beyond the discrete points where the options are quoted. Moreover, the absence of arbitrage opportunities are imposed by penalizing an associated loss function as a soft constraint. For comparison with existing approaches, the proposed method is tested on both synthetic and market option prices, which shows an improved performance in terms of reduced interpolation and reprice errors, as well as the smoothness of the calibrated local volatility. An ablation study has been performed, asserting the robustness and significance of the proposed method.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | M. Chataigner, A. Cousin, S. Crépey, M. Dixon, and D. Gueye (2021) Beyond surrogate modeling: Learning the local volatility via shape constraints | 1.000 | 11 | 5 | 100% |
| 2 | M. Chataigner, S. Crépey, and M. Dixon (2020) Deep local volatility | 1.000 | 11 | 4 | 100% |
| 3 | S. Crépey (2002) Calibration of the local volatility in a trinomial tree using Tikhonov regularization | 1.000 | 5 | 3 | 100% |
| 4 | Y. Achdou and O. Pironneau (2005) Computational Methods for Option Pricing | 0.928 | 4 | 4 | 100% |
| 5 | D. Ackerer, N. Tagasovska, and T. Vatter (2020) Deep smoothing of the implied volatility surface | 0.928 | 4 | 3 | 100% |
| 6 | B. Dupire (1994) Pricing with a smile | 0.737 | 3 | 2 | 100% |
| 7 | A. G. Baydin, B. A. Pearlmutter, A. A. Radul, and J. M. Siskind (2017) Automatic differentiation in machine learning: a survey | 0.644 | 2 | 2 | 100% |
| 8 | Z. Wang and C. Guet (2022) Self-consistent learning of neural dynamical systems from noisy time series | 0.511 | 2 | 1 | 100% |
| 9 | C. Bennett (2014) Trading Volatility, Correlation, Term Structure and Skew | 0.405 | 1 | 1 | 100% |
| 10 | A. N. Gorban and D. C. Wunsch (1998) The general approximation theorem | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 23 scored citations.