A discussion on mathematical models for option valuation

Abstract

Options as a type of financial derivatives have become increasingly popular in recent years; therefore, understanding how to value options as a derivative is crucial. To analyse the problem, we can use mathematical stochastic analysis from the perspectives of risk management and return maximisation, and then develop an option valuation model. Using a literature restatement approach, the mathematical model of option valuation is examined in this study. Bachilier introduced the option valuation model in 1900 as a breakthrough in the study of financial mathematics. In the 1860s, the asset pricing model was introduced, followed by the famous B-S formula published by F. Black and M. Scholes, which is also used to research option valuation. The above-mentioned mathematical models have been refined and are now frequently utilised in the options market. They can also be used as a criterion for buyers to determine the value of options, thus it is important to investigate this subject, which will be the subject of this paper.