RECONSTRUCTING PIECEWISE CONSTANT LOCAL VOLATILITY SURFACES

초록

In this study, we present an algorithm for reconstructing local volatility surfaces to price European call options by using piecewise constant functions. The proposed method is based on the finite difference method to find the numerical solution of the generalized Black-Scholes equation. To solve optimization problems, the MATLAB function ‘lsqcurvefit’ is used. This function is particularly effective for fitting a model to data by minimizing the sum of squared differences between the observed and the predicted prices. To illustrate the effectiveness of the proposed method, we conduct computational tests with real market data from the KOSPI200 and S&P500 indices.

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