In this paper we propose an inversion algorithm with computable error bounds for two-dimensional, two-sided Laplace transforms. The algorithm consists of two discretization parameters and two truncation parameters. Based on the computable error bounds, we can select these parameters appropriately to achieve any desired accuracy. Hence this algorithm is particularly useful to provide benchmarks. In many cases, the error bounds decay quickly (e.g., exponentially), making the algorithm very efficient. We apply this algorithm to price exotic options such as spread options and barrier options under various asset pricing models as well as to evaluate the joint cumulative distribution functions of related state variables. The numerical examples indicate that the inversion algorithm is accurate, fast and easy to implement.
"A two-dimensional, two-sided Euler inversion algorithm with computable error bounds and its financial applications." Stoch. Syst. 4 (2) 404 - 448, 2014. https://doi.org/10.1214/12-SSY094