Universality of stock option prices: an empirical result

Via examining the option prices of seven actively traded stocks (IWM, MDY, QQQQ, SPY, GOOG, MSFT, QCOM, etc.) with a phenomenological approach, we report two important discoveries in this paper. We introduce the dimensionless parameters to express the relationships among them. The first one is that, for a given day, the option prices of a stock as a function of strike prices with the same expiry date can be empirically fitted by very simple elementary functions of the underlying security, the at-the-money (ATM) prices, and one fitting parameter. The second discovery is that, for a given day, the ATM price with various expiry dates can be empirically fitted to a power-law function of the time interval from the given day to the option expiry day. The application of these discoveries is briefly discussed.