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Portfolio risk measures and option pricing under a Hybrid Brownian motion modelMbona, Innocent January 2017 (has links)
The 2008/9 financial crisis intensified the search for realistic return models, that capture
real market movements. The assumed underlying statistical distribution of financial returns
plays a crucial role in the evaluation of risk measures, and pricing of financial instruments.
In this dissertation, we discuss an empirical study on the evaluation of the traditional
portfolio risk measures, and option pricing under the hybrid Brownian motion model, developed
by Shaw and Schofield. Under this model, we derive probability density functions
that have a fat-tailed property, such that “25-sigma” or worse events are more probable. We then
estimate Value-at-Risk (VaR) and Expected Shortfall (ES) using four equity stocks listed on
the Johannesburg Stock Exchange, including the FTSE/JSE Top 40 index. We apply the historical
method and Variance-Covariance method (VC) in the valuation of VaR. Under the VC
method, we adopt the GARCH(1,1) model to deal with the volatility clustering phenomenon.
We backtest the VaR results and discuss our findings for each probability density function.
Furthermore, we apply the hybrid model to price European style options. We compare the
pricing performance of the hybrid model to the classical Black-Scholes model. / Dissertation (MSc)--University of Pretoria, 2017. / National Research Fund (NRF), University of Pretoria Postgraduate bursary and the General
Studentship bursary / Mathematics and Applied Mathematics / MSc / Unrestricted
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Jump-diffusion based-simulated expected shortfall (SES) method of correcting value-at-risk (VaR) under-prediction tendencies in stressed economic climateMagagula, Sibusiso Vusi 05 1900 (has links)
Value-at-Risk (VaR) model fails to predict financial risk accurately especially during financial crises. This is mainly due to the model’s inability to calibrate new market information and the fact that the risk measure is characterised by poor tail risk quantification. An alternative
approach which comprises of the Expected Shortfall measure and the Lognormal Jump-Diffusion (LJD) model has been developed to address the aforementioned shortcomings of VaR. This model is called the Simulated-Expected-Shortfall (SES) model. The Maximum Likelihood Estimation (MLE) approach is used in determining the parameters of the LJD model since it’s more reliable and authenticable when compared to other nonconventional parameters estimation approaches mentioned in other literature studies. These parameters are then plugged into the LJD model, which is simulated multiple times in generating the new loss dataset used in the developed model. This SES model is statistically
conservative when compared to peers which means it’s more reliable in predicting financial risk especially during a financial crisis. / Statistics / M.Sc. (Statistics)
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Jump-diffusion based-simulated expected shortfall (SES) method of correcting value-at-risk (VaR) under-prediction tendencies in stressed economic climateMagagula, Sibusiso Vusi 05 1900 (has links)
Value-at-Risk (VaR) model fails to predict financial risk accurately especially during financial crises. This is mainly due to the model’s inability to calibrate new market information and the fact that the risk measure is characterised by poor tail risk quantification. An alternative
approach which comprises of the Expected Shortfall measure and the Lognormal Jump-Diffusion (LJD) model has been developed to address the aforementioned shortcomings of VaR. This model is called the Simulated-Expected-Shortfall (SES) model. The Maximum Likelihood Estimation (MLE) approach is used in determining the parameters of the LJD model since it’s more reliable and authenticable when compared to other nonconventional parameters estimation approaches mentioned in other literature studies. These parameters are then plugged into the LJD model, which is simulated multiple times in generating the new loss dataset used in the developed model. This SES model is statistically
conservative when compared to peers which means it’s more reliable in predicting financial risk especially during a financial crisis. / Statistics / M.Sc. (Statistics)
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