Pricing discrete double barrier options with a numerical method

Abstract

Most of traded double barrier options are monitored in discrete time, their pricing being more challenging than in continuous time. A few solutions are analytical with a correction for continuity; the remaining solutions are numerical with lattices, grids or Monte Carlo (MC) simulation. We apply an original variance reduction technique to the pricing of European double barrier options monitored in discrete time. This technique speeds up significantly the MC simulation. The computational algorithm repeats each experiment with an increasing number of trials at a logarithmic rate and calculates a weighted average of the options values. We test the accuracy of the Login (Logarithmic Increment) model with an analytical solution adjusted for discretization and a naive numerical model using Monte Carlo simulation. We show that the Login model accurately prices double barrier options. Market participants in need of selecting a reliable numerical method for pricing double barrier options monitored in discrete time will find our article appealing. Moreover, the idea behind the method is simple and can be applied to the pricing of plain-vanilla or more complex derivatives, easing and speeding the valuation step significantly.