Most of the currently known option pricing techniques utilize the underlying asset price and strike price, its volatility and time to maturity, as well as the risk freerate. However, both the volatility and the risk-free rate are anticipated via the price move of the underlying asset. Looking at the same time at the Brownian motion, on which we base the modeling of the underlying asset price-move so as to value an option, we realize that its volatility is captured by the time to maturity. Moreover, the value of an option increases both as the volatility and time to maturity increase. These observations make us believe that we could find simplified option pricing formulas depending on the underlying asset (price and strike price) and the time to maturity only. The advantage of the approach is that less simplifying assumptions are needed and much simpler methods are produced. In this paper we provide alternative formulas for pricing European and American type options. We test our formulas against the Greek stock and derivatives market by applying the appropriate hypothesis testing.
