Selective Forgetting in Option Calibration: An Operator-Theoretic Gauss-Newton Framework

Modern financial models are not static; they are recalibrated as market conditions change. Therefore calibrating parametric asset-pricing models to market data has always been an ongoing interest for both practitioners and academics in the field of mathematical finance. Risk management systems along with trading desks rely heavily on the repeated solutions of inverse problems aimed at calibrating and adjusting parameters θ so that the model-based prices m(x;θ) reproduce observed quotes to some extent of accuracy. Option-implied volatility surfaces evolve minute by minute, and model parameters such as mean reversion, volatility of volatility, or correlation etc. are adapted to new market information.