On The Rate Of Convergence Of Barrier Option Prices In Binomial Market To Those In Continuous Time Market

A barrier option is a derivative with a payoff that depends on the fact whether asset price crosses certain level during certain time interval. Thus, payment for barrier option depends on the behavior of the price asset during all the time interval, i.e. barrier option is a particular case of exotic option. The simplest barrier options are calls and puts that are knocked out or knocked in by the underlying asset itself. The payoff of a knock-out option is made if underlying asset price does not cross the barrier, such options are of two types: if asset price does not cross the barrier below, then such an option is called “up-and-out”, if from above – “down-and-out”. Payoff of a knock-in option is made if underlying asset price crosses the barrier, they also are of two types accordingly: “up-and-in” and “down-and-in”. Altogether there are eight types of barrier options.