Why do we use copulas for spread options but do not use them to correlate random variables across time, such as in the forward starting option?
One is exploring forward volatility of a price of a single asset (joint distributions from within a process), the other explores correlation of two prices at the same time for two different underlyings (glueing, otherwise unrelated, marginal distributions).
Forward starting options depend on the joint distribution of the (already chosen and used to price other types of options, say Asians and continuous barriers) underlying process at two different times. The process provides consistency for pricing forward starting options for various pairs of times (and consitency with the rest of exotics depending on that process). There is no room for copula games. Once priced, one can obtain a Black-Scholes-implied forward volatility, giving a view of the forward volatility skew (one needs to explore stochastic volatility models to get sensible views, local volatility models are not sufficient).