Fast evaluation of some probability integrals arisen from the valuations of discretely monitored derivative securities

Abstract

In this paper, we propose a fast numerical method to evaluate discretely monitored derivatives. The key is to compute the involved probability integrals interactively. Our method can avoid the “curse of dimensionality” that most other methods suffer. Also, we give a constructive proof for explicit error estimation that based on a simple and systematic quadrature technique. The numerical frameworks are included for applications of barrier options on a stock and a short rate.