Reconstructing the Quadratic Local Volatility Surface for European Options

초록

In this work, we introduce a method to reconstruct quadratic local volatility surfaces for European call options. The procedure makes use of observed option prices, a calibration mechanism, and the generalized Black–Scholes model. The local volatility surface is represented by quadratic functions: at prescribed time points, second-order polynomials are defined as functions of the asset price, and the volatility at other time levels is determined by linearly connecting adjacent polynomial curves. To examine the performance of the method, we carry out numerical experiments using both artificially generated option prices and market data from several indices, including KOSPI200, S&P500, Hang Seng, Eurostoxx 50, and Nikkei 225. Numerical solutions obtained from the generalized Black–Scholes equation, together with the reconstructed quadratic volatility surfaces, exhibit close consistency with the observed market prices. © The Author(s), under exclusive licence to Springer Nature India Private Limited 2026.

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