This paper deals with the option-pricing problem. In the first part of the paper we study in more details the discrete setting of the option-pricing problem usually referred to as the binomial scheme. We highlight basic differences between the old and the new approaches. The main qualitative distinction of the new pricing approach from either binomial or Black Scholes’s is that it represents the option price as a stochastic process. This stochastic interpretation can not give straightforward advantage for an investor due to stochastic setting of the pricing problem. The new approach explicitly states that the options price is more risky than represented by binomial scheme or Black Scholes theory. Continuous setting will be considered in the second part of the paper following [1]. One significant conclusion follows from the new model. It states that there is no sense in using either neutral probabilities or ‘neutral world’ applications for options valuation either theoretically or numerically. Recall that after the Black Scholes’ publication [2] the ‘simplified’ approach named later binomial scheme was introduced in [3]. In this paper referring to the historical tradition we first represent discrete scheme. In several examples we discuss two-period plain vanilla option valuation. Then we extend the discrete scheme applications to an exotic option-pricing referred to as a compound option. The compound option in Black Scholes setting was first studied in [4] and then in [5,6]. To highlight the difference between stochastic and deterministic option price definitions note that if a deterministic value is interpreted as a perfect or fair price we can comment that the stochastic interpretation provides this number or any other with the probability that real world option value at maturity will be bellow chosen number. This probability is a pricing risk of the option. Thus with an investor’s motivation of the option pricing the stochastic approach gives information about the risk taking. The investor analyzing option price and corresponding risk makes a decision to purchase the option or not. As far as this paper presents alternative point on option pricing it might be useful to present a short history of this development. Recall that according the US law institutions must provide clients by the risk information regarding client’s prospective on their investments. This circumstance implies importance new approach measuring risk of investments. Different parts of this paper were submitted and sent to journals, conferences, and prominent professors. The third part of the paper was sent to Federal Reserve from the Congressman office and simple examples showing drawbacks of the benchmark option valuation method were submitted to SEC in August 2002.