The Black Scholes model was developed by Fischer Black and Myron Scholes in 1973. It is based on a number of simplifying assumptions such as underlying stock prices following a geometric Brownian motion with constant drift and volatility, no-arbitrage, no dividends, no transaction costs, borrowing and lending at a constant risk free interest rate, unlimited as well as fractional purchases and sales. From this model they derived the Black Scholes equation which models the price of an option over time. The Black Scholes formula for determining the price of a European call or put option is obtained by solving the Black Scholes equation by applying certain terminal and boundary conditions to it. The value of the options based on the formula are functions of time to maturity, price of underlying asset, exercise or strike price, risk free interest rate and constant volatility.
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