  The use of sequential Monte Carlo within simulation for path-dependent option
pricing is proposed and evaluated. Recently, it was shown that explicit
solutions and importance sampling are valuable for efficient simulation of spot
price and volatility, especially for purposes of path-dependent option pricing.
The resulting simulation algorithm is an analog to the weighted particle
filtering algorithm that might be improved by resampling or branching. Indeed,
some branching algorithms are shown herein to improve pricing performance
substantially while some resampling algorithms are shown to be less suitable in
certain cases. A historical property is given and explained as the
distinguishing feature between the sequential Monte Carlo algorithms that work
on path-dependent option pricing and those that do not. In particular, it is
recommended to use the so-called effective particle branching algorithm within
importance-sampling Monte Carlo methods for path-dependent option pricing. All
recommendations are based upon numeric comparison of option pricing problems in
the Heston model.
