Title: Pattern derivatives

Authors: Casey S. Schroeder; Massimo Di Pierro

Addresses: School of Computing, DePaul University, CDM Center, 243 South Wabash Avenue, Chicago, IL, USA. ' School of Computing, DePaul University, CDM Center, 243 South Wabash Avenue, Chicago, IL, USA

Abstract: In this paper, we propose a new type of derivative called a pattern derivative. In the simple case of an asset that moves up u or down d in value, a pattern is a sequence of {u, d} movements that may occur before expiration. We provide general pricing formulas that rely on a brute force approach as well as efficient valuation algorithms based on recursive formulas for the probability of patterns to occur. We generalise our results to exclusive, inclusive, and multi-pattern options. Finally, we discuss the possible benefits of this type of options.

Keywords: patterns; pattern derivatives; options pricing.

DOI: 10.1504/IJFMD.2011.045608

International Journal of Financial Markets and Derivatives, 2011 Vol.2 No.4, pp.249 - 257

Available online: 23 Feb 2012 *

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