  This papers addresses the stock option pricing problem in a continuous time
market model where there are two stochastic tradable assets, and one of them is
selected as a num\'eraire. It is shown that the presence of arbitrarily small
stochastic deviations in the evolution of the num\'eraire process causes
significant changes in the market properties. In particular, an equivalent
martingale measure is not unique for this market, and there are non-replicable
claims. The martingale prices and the hedging error can vary significantly and
take extreme values, for some extreme choices of the equivalent martingale
measures. Some rational choices of the equivalent martingale measures are
suggested and discussed, including implied measures calculated from observed
bond prices. This allows to calculate the implied market price of risk process.

Pricing of Securities;Probability;Computational Finance