Toward the theory of pricing of options of both European and American types. I. 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 $B=(B_n )_{n\ge 0}$ and risky stock $S=(S_n )_{n\ge 0}$, 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.