TEOREMA FUNGSI INVERS DAN APLIKASINYA DALAM ESTIMASI VOLATILITAS MODEL STOKASTIK

Abstract

The Inverse Function Theorem plays a fundamental role in various areas of applied mathematics, particularly in stochastic analysis and financial modeling. This article provides a systematic proof of the theorem and explores its application in estimating volatility within stochastic models. By leveraging a stochastic transformation based on the inverse function, volatility in the Black-Scholes model is reconstructed directly from historical stock price data without imposing explicit distributional assumptions. This methodology is reinforced through the discretization of stochastic integrals and numerical simulations implemented using the R programming language. The simulation results demonstrate that volatility estimates derived from this approach are comparable to conventional methods such as Maximum Likelihood Estimation (MLE), while offering improved computational efficiency. Moreover, the findings indicate that the inverse function theorem can be utilized as a powerful tool for extracting hidden parameters in stochastic systems. This has significant implications for financial risk analysis, option pricing models, and broader financial market modeling, providing a robust alternative for understanding and predicting market behavior.