The Hurst parameter and option pricing with fractional Brownian motion
In the mathematical modeling of the classical option pricing models it is assumed that the underlying stock price process follows a geometric Brownian motion, but through statistical analysis persistency was found in the log-returns of some South African stocks and Brownian motion does not have pers...
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University of Pretoria
2013
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| Online Access: | http://hdl.handle.net/2263/26521 Ostaszewicz, AJ 2012, The Hurst parameter and option pricing with fractional Brownian motion, MSc dissertation, University of Pretoria, Pretoria, viewed yymmdd < http://hdl.handle.net/2263/26521 > http://upetd.up.ac.za/thesis/available/etd-02012013-134807/ |
| Summary: | In the mathematical modeling of the classical option pricing models it is assumed that the underlying stock price process follows a geometric Brownian motion, but through statistical analysis persistency was found in the log-returns of some South African stocks and Brownian motion does not have persistency. We suggest the replacement of Brownian motion with fractional Brownian motion which is a Gaussian process that depends on the Hurst parameter that allows for the modeling of autocorrelation in price returns. Three fractional Black-Scholes (Black) models were investigated where the underlying is assumed to follow a fractional Brownian motion. Using South African options on futures and warrant prices these models were compared to the classical models. === Dissertation (MSc)--University of Pretoria, 2012. === Mathematics and Applied Mathematics === unrestricted |
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