Continuous time Markov chain (CTMC) approximation is an intuitive and powerful method for pricing options in general Markovian models. This paper analyzes how grid design affects the convergence behavior of barrier and European options in general diffusion models. Using the spectral method, we...

Diffusion models with non-smooth coefficients often appear in financial applications, with examples including but not limited to threshold models for financial variables, the pricing of occupation time derivatives and shadow rate models for interest rate dynamics. To calculate the expected value...

Calculation of the expected value of discounted payoffs with possible monitoring of barrier crossing under one-dimensional diffusion models is required in many applications. Markov chain approximation is a computationally efficient approach for this problem. This paper undertakes the challenge...