Pricing Discretely Monitored Barrier Options by a Markov Chain

The method here to price discretely monitored barrier options in both constant and time-varying volatility valuation frameworks uses a time-homogeneous Markov chain to approximate the underlying asset price process. It provides a natural framework for this pricing process because the discrete time step of the Markov chain can be easily matched with the monitoring frequency of the barrier. The underlying asset price can also be partitioned so as to place the barrier suitably. The method can efficiently handle difficult cases where the barrier is close to the initial asset price. Examples include both knock-in and knock-out barrier options. Different types of barriers such as single, double, and moving barriers are also analyzed