TOWARD THE THEORY OF PRICING OF OPTIONS OF BOTH EUROPEAN AND AMERICAN TYPES .1. DISCRETE-TIME

This paper consisting of two parts (I - discrete time, II - continuous time [19]) considers the main concepts, statements of problems, and results of financial mathematics in connection with options and option contract pricing as a kind of derivative securities. In 1 it is assumed that the contracts are exercised in discrete (B, S)-market. There are two assets: riskless bank account B = (B-n)(n greater than or equal to 0) and risky stock S = (S-n)(n greater than or equal to 0), European as well as American options are examined. Special attention is paid to the ''martingale'' methods of option pricing and hedging strategies in particular for call options and put options.