Title: Universality of stock option prices: an empirical result

Authors: Z.J. Yang, Angel Yang

Addresses: Efficient Capital Management, 5th Avenue Station, 300 East 5th Avenue, Naperville, IL 60563, USA. ' 1304 Cantigny Ct., Naperville, IL 60565, USA

Abstract: 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.

Keywords: stock option prices; universality; scaling; financial markets.

DOI: 10.1504/IJFMD.2010.032467

International Journal of Financial Markets and Derivatives, 2010 Vol.1 No.2, pp.169 - 174

Published online: 03 Apr 2010 *

Full-text access for editors Access for subscribers Purchase this article Comment on this article