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Calibration of the subdiffusive Black–Scholes model

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  • Sebastian Orzel
  • Aleksander Weron

Abstract

In this paper we discuss subdiffusive mechanism for the description of some stock markets. We analyse the fractional Black–Scholes model in which the price of the underlying instrument evolves according to the subdiffusive geometric Brownian motion. We show how to efficiently estimate the parameters for the subdiffusive Black–Scholes formula i.e. parameter alpha responsible for distribution of length of constant stock prices periods and sigma — volatility parameter. A simple method how to price subdiffusive European call and put options by using Monte Carlo approach is presented.

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File URL: http://www.im.pwr.wroc.pl/~hugo/RePEc/wuu/wpaper/HSC_09_02.pdf
File Function: Original version, 2009
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Bibliographic Info

Paper provided by Hugo Steinhaus Center, Wroclaw University of Technology in its series HSC Research Reports with number HSC/09/02.

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Length: 11 pages
Date of creation: 2009
Date of revision:
Publication status: Published in Acta Physica Polonica B 41 (5), 1151-1159 (2010).
Handle: RePEc:wuu:wpaper:hsc0902

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Related research

Keywords: Black-Scholes model; option price; Monte Carlo simulation; fractional Fokker-Planck Equation; time-changed Brownian motion; martingale measure;

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Cited by:
  1. Sebastian, Orzeł & Agnieszka, Wyłomańska, 2010. "Calibration of the subdiffusive arithmetic Brownian motion with tempered stable waiting-times," MPRA Paper 28593, University Library of Munich, Germany.

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