An inverse algorithm with the Levenberg-Marquardt method is developed to estimate the time-dependent volatility function that was used in the model of financial analysis for European options from the observed value of option price. Numerical experiments for the inverse algorithm are performed to show the validity of the present study. Moreover, the statistical analysis is also considered here to determine the standard deviation and 99% confidence bounds for the estimated volatility function. Results show that the standard deviations of the estimated volatility function are decreased as the time approaches the expiry date. This implies that a more reliable volatility function can be obtained as time approaches the expiry date.
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