The Black-Scholes Model

Black-Scholes Model Now what exactly is Black-Scholes Model? The Black-Scholes model came to be when Fischer Black and Myron Scholes underwent Research to find a better option pricing strategy in \cite{BS-1973}. The Black-Scholes Model is used to calculate the theoretical price of a European call or put option, ignoring any dividends paid during the options lifetime. The Black-Scholes model assumes that the option can be exercised only at expiration and that it requires both the risk-free rate and the volatility of the underlying stock price remain constant over the period of analysis. The Black-Scholes model also assumes that it follows a lognormal distribution, and hence the returns on the underlying asset are normally distributed. In

Black-Scholes and Merton reaches the study of a dynamic trading strategy in the underlying stock that exactly replicates the option contract payoff. Therefore Arbigtrage arguments make is possible to obtain the theoretical price of the option as the discounted expected value of its pay-off at maturity with respect to risk-neutral measure. Another feature of the Black-Scholes model and Mertons study is that the trading is assumed to be made in a continuous manner so that any option does not depend on the investors risk preferences, although this assumption is yet still an idea rather than actual event as it impossible in actual

These days, mathematical programmes and calculators have been designed to input the data given and calculate the necessary results using whatever model the investors or companies choose. Even when all these additives have been created to make life easier, the Black-Scholes model is still highly implemented in daily uses, such as Field of weather derivatives in \cite{Zeng-2000}. So due to empirical and theoretical studies of the Black-Scholes model its concluded that it is very predictive, meaning that it will generate an option price that is very close to the actual price at which options