Pricing of options under different volatility models

In this paper we compare the price of an option with one year maturity of the German stock index DAX for several volatility models including long memory and leverage effects. We compute the price by applying a present value scheme as well as the Black-Scholes and Hull-White formulas which includes stochastic volatility. We find that long memory as well as asymmetry affect the Black-Scholes price significantly whereas the Hull-White price is hardly affected by long memory but still by including asymmetries.