The efficient solution of linear complementarity problems for tridiagonal Minkowski matrices
ACM Transactions on Mathematical Software (TOMS)
A Finite Difference Scheme for Option Pricing in Jump Diffusion and Exponential Lévy Models
SIAM Journal on Numerical Analysis
Accurate Evaluation of European and American Options Under the CGMY Process
SIAM Journal on Scientific Computing
Some Convergence Results for Howard's Algorithm
SIAM Journal on Numerical Analysis
A Numerical Analysis of American Options with Regime Switching
Journal of Scientific Computing
An iterative method for pricing American options under jump-diffusion models
Applied Numerical Mathematics
A Finite Time Horizon Optimal Stopping Problem with Regime Switching
SIAM Journal on Control and Optimization
Methods for Pricing American Options under Regime Switching
SIAM Journal on Scientific Computing
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A theoretical analysis tool, iterated optimal stopping, has been used as the basis of a numerical algorithm for American options under regime switching (Le and Wang in SIAM J Control Optim 48(8):5193---5213, 2010). Similar methods have also been proposed for American options under jump diffusion (Bayraktar and Xing in Math Methods Oper Res 70:505---525, 2009) and Asian options under jump diffusion (Bayraktar and Xing in Math Fin 21(1):117---143, 2011). An alternative method, local policy iteration, has been suggested in Huang et al. (SIAM J Sci Comput 33(5):2144---2168, 2011), and Salmi and Toivanen (Appl Numer Math 61:821---831, 2011). Worst case upper bounds on the convergence rates of these two methods suggest that local policy iteration should be preferred over iterated optimal stopping (Huang et al. in SIAM J Sci Comput 33(5):2144---2168, 2011). In this article, numerical tests are presented which indicate that the observed performance of these two methods is consistent with the worst case upper bounds. In addition, while these two methods seem quite different, we show that either one can be converted into the other by a simple rearrangement of two loops.