Title: A model of stock option prices

Authors: Zhongjin Yang; Cassidy Yang

Addresses: Efficient Capital Management, 4355 Weaver Parkway, Warrenville, IL 60555, USA. ' Naperville Central High School, Naperville, IL 60540, USA

Abstract: We postulate that the first order derivative (delta) of the stock option is a logistic function, which is widely used for modelling growth phenomena with bounded conditions in natural and social sciences. The integration of the logistic function yields the universal description (formula) of the option price, which was reported previously. The universal formula shows very good scaling properties that can be used to rescale many stock option prices into one unique curve with only one scaling parameter. The model was tested by examining several widely traded stocks in recent years. As examples, we have successfully rescaled the prices into the universal curve even for the huge market moves, e.g., 2008-09-29 [on the day: DJI down 777.68 (-7%) and SP500 down 106.85 (-9%)] and 2008-10-13 [DJI up 936.42 (11%) and SP500 up 104.13 (12%)].

Keywords: option prices; universality; scaling; financial markets; logistic distribution; modelling; stock options.

DOI: 10.1504/IJFMD.2011.045599

International Journal of Financial Markets and Derivatives, 2011 Vol.2 No.4, pp.288 - 297

Published online: 28 Feb 2015 *

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