Before revision:  We show that the the joint distribution of any finite sequence of log returns admits a Gram-Charlier A expansion in closed-form . We use this to derive closed-form series representations for option prices whose payoff is a function of the underlying asset price trajectory at finitely many time points.
After revision:  We show that the the joint distribution of any finite sequence of log returns admits a Gram-Charlier A expansion in closed-form coefficients. We derive closed-form series representations for option prices whose payoff is a function of the underlying asset price trajectory at finitely many time points.