Modeling Of Returns And Option Pricing Using Models With Flexible Volatility

This work deals with time series with flexible conditional variance which is changing according to past observations and values of past volatilities. We consider a class of ARCH-type models as a special case of GARCH models and its extension GARCH-M  Stationarity, estimation procedures, and LM tests are discussed. Further, we apply the models to financial data from the Czech capital market forecasting stock returns and estimating option prices. We present an extension of option pricing using equivalent martingale measure which special case leads to the well-known Black-Scholes formula.