There has been introduced the Black-Scholes, Binomial, And Monte Carlo models, and for European option with Underlying price of 1008, Strike price 1020, Time to maturity of 33 days, annualized volatility of 0.277 and risk-free rate of return and cost of carry of 0.0610 I made the calculation by each model as following: Black-Scholes: call option = 304915, put option= 38.88161 Binomial: with 3 steps: call= 32.97069, put= 39.3608 Monte Carlo: call= call= 30 56437, put= 37.01675 And showed in almost 75 steps Binomial prices tends to Black-Scholes. Calculated Greeks and figured how Delta changes with respect to stock price. Figured the Volatility smile and seen volatility is not constant unlike the assumption of the model using Black-Scholes, and seen it increases as the option came increasingly in the money. Made some standard error of Monte Carlo model calculation for different number of simulation, and then made calculation of knock-in and knock-out calculation for specific barrier level with no rebate paying and seen the prices of them (cui, cuo, cdi, cdo, pui, puo pdi, pdo) changes with respect to different barriers and also seen the sum of In-and-Out prices are as Black-Scholes price, in R mostly by usage of fOptions and fExoticOptions packages.