Title: A note on intraday option pricing

Authors: Enrico Scalas; Mauro Politi

Addresses: Dipartimento di Scienze e Innovazione Tecnologica, Università del Piemonte Orientale, Viale T. Michel 11, 15121, Alessandria, Italy; BCAM, Basque Centre for Applied Mathematics, Alameda de Mazarredo 14, 48009 Bilbao, Bilbao, Basque Country, Spain ' BCAM, Basque Centre for Applied Mathematics, Alameda de Mazarredo 14, 48009 Bilbao, Bilbao, Basque Country, Spain

Abstract: Compound renewal processes can be used as an approximate phenomenological model of tick-by-tick price fluctuations. An exact and explicit general formula is derived for the martingale price of a European call option written on a compound renewal process. The option price is obtained using the direct method of indicator functions. The applicability of this result is discussed.

Keywords: option pricing; high-frequency finance; high-frequency trading; computer trading; jump-diffusion models; pure-jump models; continuous-time random walks; semi-Markov processes; price fluctuations; martingale price; European call options; compound renewals.

DOI: 10.1504/IJANS.2013.052763

International Journal of Applied Nonlinear Science, 2013 Vol.1 No.1, pp.76 - 86

Received: 25 Sep 2012
Accepted: 25 Sep 2012
Published online: 30 Jul 2014 *

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