Calibration of the subdiffusive Black–Scholes model
AbstractIn 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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Bibliographic InfoPaper provided by Hugo Steinhaus Center, Wroclaw University of Technology in its series HSC Research Reports with number HSC/09/02.
Length: 11 pages
Date of creation: 2009
Date of revision:
Publication status: Published in Acta Physica Polonica B 41 (5), 1151-1159 (2010).
Black-Scholes model; option price; Monte Carlo simulation; fractional Fokker-Planck Equation; time-changed Brownian motion; martingale measure;
Find related papers by JEL classification:
- C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
- C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
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- 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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