On The Rate Of Convergence Of Prices Of Barrier Options With Discrete And Continuous Time

A barrier option is a derivative realized or cancelled if the price of the underlying asset crosses a certain barrier. Most of the models in financial mathematics are considered for markets with continuous time. However the trading days for a particular stock take place at separate moments, i.e. discretely. The Black–Scholes model is extended in the paper in the sense that we consider barrier options with varying drifts. We find the rate of convergence of prices of such options with discrete time to the prices of options with continuous time.