Comment on 'Correcting for Simulation Bias in Monte Carlo Methods to Value Exotic Options in Models Driven by Levy Processes' by C. Ribeiro and N. Webber

Ribeiro and Webber (2006) propose a method to correct for simulation bias in the Monte Carlo valuation of options with pay-offs depending on the extreme value(s) of the underlying which is driven by a special Levy process, namely a normal inverse Gaussian (NIG) or a variance gamma (VG) process. The proposed method was already successfully used by Beaglehole et al. (1997) and El Babsiri and Noel (1998) when the underlying follows a Brownian motion. Unfortunately, Ribeiro and Webber, in their attempt to exploit well-known subordinator representations of NIG and VG processes, overlook the fact that these subordinator representations lead to discontinuous subordinators. Therefore their correction method 'overcorrects' the simulation bias by magnitudes, resulting in a much bigger simulation bias with reversed sign. We point out where the assumption of a continuous subordinator is implicitly used in the paper of Ribeiro and Webber (2006). Furthermore, by applying the unbiased Monte Carlo valuation approach for Barrier options under VG models of Becker (2009) to the barrier and lookback options considered in Ribeiro and Webber (2006), we show that the newly introduced simulation bias exceeds the corrected simulation bias by far.