Calibration of the subdiffusive Black–Scholes model

Sebastian Orzeł and Aleksander Weron

No HSC/09/02, HSC Research Reports from Hugo Steinhaus Center, Wroclaw University of Science and Technology

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.

Keywords: Black-Scholes model; option price; Monte Carlo simulation; fractional Fokker-Planck Equation; time-changed Brownian motion; martingale measure (search for similar items in EconPapers)
JEL-codes: C46 C53 G13 (search for similar items in EconPapers)
Pages: 11 pages
Date: 2009
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Published in Acta Physica Polonica B 41 (5), 1151-1159 (2010).

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http://www.im.pwr.wroc.pl/~hugo/RePEc/wuu/wpaper/HSC_09_02.pdf Original version, 2009 (application/pdf)

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Persistent link: https://EconPapers.repec.org/RePEc:wuu:wpaper:hsc0902

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