  Option valuation problems are often solved using standard Monte Carlo (MC)
methods. These techniques can often be enhanced using several strategies
especially when one discretizes the dynamics of the underlying asset, of which
we assume follows a diffusion process. We consider the combination of two
methodologies in this direction. The first is the well-known multilevel Monte
Carlo (MLMC) method, which is known to reduce the computational effort to
achieve a given level of mean square error relative to MC in some cases.
Sequential Monte Carlo (or the particle filter (PF)) methods have also been
shown to be beneficial in many option pricing problems potentially reducing
variances by large magnitudes (relative to MC). We propose a multilevel
particle filter (MLPF) as an alternative approach to price options. The
computational savings obtained in using MLPF over PF for pricing both vanilla
and exotic options is demonstrated via numerical simulations.
