Cutting edge introduction

Most models are specified in continuous time form, but this can cause discrepancies and convergence headaches when implementing multiple numerical methods for different functions. Laurie Carver introduces this month’s technical section by looking at the benefits of having several consistent but discrete models

Perhaps the most convenient fiction in financial modelling is the assumption that markets trade in continuous time, with asset price processes solving stochastic differential equations (SDEs). The assumption is as old as the subject itself, having begun with Louis Bachelier formulating his Brownian motion model in 1900, five years before Einstein discovered it in physics.

The trouble comes when an attempt is made to capture this in the inherently discrete world of the computer. Whether it is