| Abstract: | A wide variety of computational schemes have been proposed for the numerical valuation of various classes of options. Experiences in numerical computation have revealed that the details of the implementation of the auxiliary conditions in the numerical algorithms may have profound effects on numerical accuracy. Difficulties in designing algorithms that deal with the path‐dependent payoffs, monitoring features, etc., have been well reported in the literature. In this article, the theoretical issues on the assessment of numerical schemes with regard to accuracy of approximation of auxiliary conditions, rate of convergence, and oscillation phenomena are reviewed. In particular, the oscillation phenomena in bond‐price calculations and the intricacies in implementing the auxiliary conditions in barrier options, proportional step options, and lookback options are discussed. With different types of options and modes of monitoring (continuous or discrete), the optimal method of placing the lattice nodes with reference to the boundary (absorbing or reflecting) are examined in order to achieve linear temporal rate of convergence. © 2001 John Wiley & Sons, Inc. Jrl Fut Mark 21:875–903, 2001 |
