Calibration of the subdiffusive Black–Scholes model
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.
|Date of creation:||2009|
|Date of revision:|
|Publication status:||Published in Acta Physica Polonica B 41 (5), 1151-1159 (2010).|
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- Simon Hurst & Eckhard Platen & Svetlozar Rachev, 1997. "Subordinated Market Index Models: A Comparison," Asia-Pacific Financial Markets, Springer, vol. 4(2), pages 97-124, May.
- Aleksander Janicki & Aleksander Weron, 1994. "Simulation and Chaotic Behavior of Alpha-stable Stochastic Processes," HSC Books, Hugo Steinhaus Center, Wroclaw University of Technology, number hsbook9401.
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