Pricing Discretely Monitored Barrier Options by a Markov Chain

We propose a Markov chain method for pricing discretely monitored barrier options in both the constant and time-varying volatility valuation frameworks. The method uses a time homogeneous Markov Chain to approximate the underlying asset price process. Our approach provides a natural framework for pricing discretely monitored barrier options because the discrete time step of the Markov chain can be easily matched with the monitoring frequency of the barrier. Furthermore the underlying asset price can also be partitioned to have the barrier suitably placed. Our method is fast, flexible and easy to implement as it reduces the pricing of American and European barrier options to simple matrix operations. Our method can efficiently handle the difficult cases where the barrier is close to the initial asset price. We study both knock-in and knock-out barrier options. Different types of barriers such as single, double and moving barriers are also analyzed.
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