Abstract:
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.
