Using a simple integral identity, we derive general expressions for the Laplace transform of the transition density of the process, if killing or reflecting boundaries are specified. We also obtain a number of useful expressions for the Laplace transforms of some functions of first-passage times...

This paper provides a survey of recent numerical methods for pricing derivative securities. Methods for standard American options on a single underlying asset, barrier and lookback options and options on multiple assets are reviewed. Criteria for comparison of different approaches are discussed....

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...