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An empirical application of Black and Scholes option pricing with fractional Brownian motion

Ramic, Armin; Paulshus, Ove
Master thesis
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Preliminary Master thesis.pdf (893.2Kb)
URI
http://hdl.handle.net/11250/2578065
Date
2018
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  • Master of Science [1823]
Abstract
This thesis examines the empirical properties of a fractional Black and Scholes model

developed by Röstek and Schobel. The model is tested and compared to the standard Black

and Scholes for Standard and Poor’s 500 call options in the period 10th May to 10th of July

2018. We first go through the theoretical differences of using a geometrical and a fractional

Brownian motion. We test the models using three different empirical tests, following the

methods of Bakshi, Cao & Chen (1997). The performance is measured using an in-sample

test, an out of sample test and running a dynamic delta hedging strategy over a period of 41

trading days. While testing the models, we highlight the importance of estimating the correct

Hurst value (long-term dependence) as the model becomes time dependent. We find that the

fractional Black and Scholes model is misspecified, but performs slightly better in the out of

sample test. In total, we rank the fractional equal to the geometric model.
Description
Masteroppgave(MSc) in Master of Science in Business, Finance - Handelshøyskolen BI, 2018
Publisher
Handelshøyskolen BI

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