Volatility is one of the biggest topics in finance today. It is the most important measure of risk and plays a crucial role in the valuation of derivatives. Volatility estimations are therefore essential in most financial decisions. However, it has been proven extremely difficult to model and forecast the volatility one witnesses in time series. This book compares two volatility models, their properties and their performances. The models compared are the GARCH model and the Markov Switching Multifractal model, two models that rely on completely different assumptions. This book assesses how both models perform in replicating financial time series. The model parameters are estimated on historical returns and option prices. The results are used to produce volatility forecasts which in their turn are evaluated in a Value at Risk setup. The analysis done shows some unexpected conclusions and promising leads for further research. This book provides a step by step manual on how to estimate various volatility models and how resulting estimates can be used for derivative pricing. This is extremely valuable for practitioners and others interested in modeling volatility in financial markets.