In our work we propose an option pricing model based on the Ornstein-Uhlenbeck process. In the quantum game theory Ornstein-Uhlenbeck process has the interpretation of non-unitary tactics. It is a fresh look at the option pricing which is grounded on the quantum game theory and it is more subtle. We show the differences between a classical look which is price changing by a Wiener process and the pricing supported by a quantum model. These differences are visible for very liquid financial instruments. We present the usage of this process to model short term structure of interest rates. In the first section we will quote the logarithmic equation which fulfils the logarithmic stock price and we will find the formula for these prices. In the second section we will succeed in finding the European option price supported by Wiener-Bachelier model and we will succeed in receiving the famous formula of Black-Scholes (whose creators won the Nobel Price in 1997). Next, we will give the probability analogous like in the first section, but it will be supported by Ornstein-Uhlenbeck process. In the fourth section we will present the Vasicek’s Model based on the Ornstein-Uhlenbeck process. In the fifth section we will find a model referring to quantum model, which describes the European option pricing. And finally we will compare the classical look at modeling option pricing based on the Wiener process and its quantum extension based on the Ornstein-Uhlenbeck process. Quantum market games broaden our horizons and quantum strategies create unique opportunities for making profits during intervals shorter than the characteristic thresholds for an effective market (Brownian motion). On such market prices behave like Rayleigh particles approaching equilibrium state. Observations of the prices on the quantum market can result in quantum Zeno effect, which should broaden the range of correctness of the market description in the mezzo-scale.

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1. Deterministic view of the capital risk