Data-Driven Periodic and Nonlinear Trends in Option Pricing: A Curve-Fitting Perspective

Abstract

This study presents a novel curve-fitting tuned methodology to model dynamic trends in data-driven option prices using various fitting models such as polynomial, exponential, Gaussian, and Fourier. It addresses the challenges of pricing options through mathematical modelling, analysing stock price uncertainties, and identifying the best trend fit. The proposed model captures trends and variability in the data, enabling the extraction of critical insights such as the rate of stock price changes over time and the ability to forecast future option prices. Using traded data from various sectors for stock prices between 13.11.2017 and 9.8.2019, statistical measures such as R-squared error, Sum of Squares Error (SSE), Degrees of Freedom Error (DFE), Adjusted R-squared, Root Mean Squared Error (RMSE), and parameter coefficients were evaluated for each model.