Small dimension PDE for discrete Asian options

This paper presents an efficient method for pricing discrete Asian options in presence of smile and non-proportional dividends. Using an homogeneity property, we show how to reduce an n0 dimensional problem to a one- or two-dimensional one. We examine different numerical specifications of our dimension reduced PDE using a Crank–Nicholson method (interpolation method, grid boundaries, time and space steps) as well as the extension to the case of non-proportional discrete dividends, using a jump condition. We benchmark our results with Quasi Monte-Carlo simulation and a multi-dimensional PDE