Mathematicaly analysis of the pricings of financial derivatives

The mathematical structure of the financial derivatives was studied. The structure of futures and options, which are the main objects of the financial derivatives, and their pricings were expressed by using mathematical models. In the studying of the mathematical structure of the financial derivatives the main properties of statistics, probability theory and linear programming were used. Also the geometric brown motions were utilized which is a stochastic process. The property that the prices of forwards and futures are equal if the interest rate is constant, was expressed as a theorem and it was proved. The futures transactions on stocks index, foreign money, commerce goods, bonds were modelled in mathematical formulations. The hedgings in futures transactions were expressed mathematically. The minimizing of the variance of the hedging was expressed as a theorem and it was proved. Also the optimal number of futures contracts was obtained mathematically. In the pricing of options contracts the geometric brown motions and the arbitrage theorem were used. Options scenarios on stock index were studied by multi binomial models. The Black?Scholes equations, which don?t let any arbitrage, are obtained. The hedging methods delta, theta, vega and rho on options contracts were expressed in mathematical formulations. Keywords: Financial derivatives, forwards, futures, options, hedging, geometric brown motions, bonds, arbitrage, Black?Scholes equations, delta, theta, vega, rho.