REFET POLAT2025-10-2220091.C. Albenese S. Jainmngal and D. Rubinsov \"The Model of lines for Option Pricing with Jump\". 2001.2.F. Black and M. Scholes \"The pricing of options and corporate liabilities. Journal of Political Economy. 81 637-59 1973.3.M. Brennan and E. Schwartz. \"The valuation of American put options. Journal of Finance. 19774.M. Brennan and E. Schwartz. \"Finite-difference methods and jump processes arising in the Pricing of contingent claims: A synthesis Journal of Financial and Quantitative Analysis. 19785.G. Courtadon. \"A more accurate finite difference approximation for the valuation of Options Journal of Financial and Quantitative Analysis 19826.H. P Me Kean Appendix \"A Free Boundary Problem for the Heat Equation Arising from a Problem in Mathematical Economics.\" Industr. Manage. Rev. 6: 32-39 1965.7.Hull John \"Options Future and other Derivative Securities\" Willeys 1997. 8.J. J McCutcheon-W. F. Scott. \"An Introduction to the Mathematics of Finance\" 1989.9.P. Van Moerbeke. \"On Optimal Stopping and Free Boundary Problem\" Arch. Rational Mech. And. 60: 101-148 1976.10.S. Sukha \"Finite-Difference Methods for Pricing the American Put Options\" 2001.11.W. Allegretto G. Barone-Adesi and R. J. Elliot \"Numerical Evaluation of the Critical Price and American Options\" Europen J. Finance 1: 69-78 1995.12.Wilmott Paiil-Dewynne. Jeff-Howison Sam \"Option Pricing Mathematical Modals and Computation\" Oxford Financial Press. 1998.13.Wilmott Paul-Dewynne Jeff-Howison Sam \"The Mathematics of Financial Derivatives\" A student Introduction 1997.1302-7980https://gcris.yasar.edu.tr/handle/123456789/11270In this paper we analyzed Options and Black -Scholes Models for the valuing and pricing of commodities. In particular we examined the numerical solution techniques of American Option Problems. For the comparison of the results pertaining to different methods we used classical methods utilizing chronological order. Then we compared the results of these methods and tried to determine the most efficient method.İngilizceİşletme FinansArticle