Abstract
In this paper, we propose a robust and accurate reconstruction algorithm for the time-dependent continuous volatility function using observed option prices from the financial market and the Black–Scholes (BS) equation. The proposed algorithm consists of two steps: First, a time-dependent piecewise-constant volatility function is calculated. Second, a continuous volatility function is reconstructed by continuously connecting the jumps of the piecewise-constant volatility values at the expiration dates. We validate the accuracy and robustness of the proposed reconstruction of time-dependent continuous volatility by employing manufactured volatility and real financial market price data.
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Data are available from the corresponding author upon reasonable request.
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Acknowledgements
The corresponding author (J.S. Kim) was supported by the Brain Korea 21 FOUR through the National Research Foundation of Korea funded by the Ministry of Education of Korea. The authors are grateful to the reviewers for constructive and helpful comments on the revision of this article.
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Hwang, Y., Lee, T., Kwak, S. et al. Robust and accurate reconstruction of the time-dependent continuous volatility from option prices. Comp. Appl. Math. 43, 307 (2024). https://doi.org/10.1007/s40314-024-02837-w
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DOI: https://doi.org/10.1007/s40314-024-02837-w