Discussion Paper

No. 2012-14 | February 15, 2012
A Parsimonious Model for Intraday European Option Pricing


A stochastic model for pure-jump diffusion (the compound renewal process) can be used as a zero-order approximation and as a phenomenological description of tick-by-tick price fluctuations. This leads to an exact and explicit general formula for the martingale price of a European call option. A complete derivation of this result is presented by means of elementary probabilistic tools.

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Cite As

Enrico Scalas and Mauro Politi (2012). A Parsimonious Model for Intraday European Option Pricing. Economics Discussion Papers, No 2012-14, Kiel Institute for the World Economy. http://www.economics-ejournal.org/economics/discussionpapers/2012-14

Comments and Questions

Anonymous - Referee Report 1
February 22, 2012 - 15:23

See attached file

Enrico Scalas - Reply to referee report
March 07, 2012 - 22:27

Dear Referee,

thanks for your useful comments on our paper. Based on your report, we will take the following main actions:

1. We will write a detailed tutorial appendix on the indicator function method and we will remove equations from 7 to 9 from the main text.

... />2. We will remove the discussion on the intra-day interest rate and place it in an appendix.

3. We will include an appendix on the model discussed in Scalas (2007), in order to show how the method presented in our paper can be adapted to that case. This task will take some time.

Then, we will further discuss the i.i.d. hypothesis and the flexibility of the model within the main text. Finally, we will correct all the misprint that you noticed and other errors that we may be able to detect.

Best regards

Enrico Scalas & Mauro Politi

Anonymous - Referee Report 2
April 19, 2012 - 11:59

See attached file

Enrico Scalas - Reply to referee 2
June 12, 2012 - 15:58

Please, see the attached file.

Enrico Scalas - A short note on multiplicative processes subordinated to renewal counting processes
December 14, 2018 - 18:23

This note is an erratum on equation (14) for the paper A Parsimonious Model for Intraday European Option Pricing by Mauro Politi and myself, available as a discussion paper at
and later published as Scalas, Enrico and Politi, Mauro (2013) A note on intraday option pricing. International
Journal ...[more]

... of Applied Nonlinear Science, 1 (1). pp. 76-86. ISSN 1752-2862.
Comments welcome!