Here is the way I think about it.A conventional forward contract on an asset S(t) is an agreement todeliver S(T) at time T > t for a fixed strike K. The strike is chosen so there isno initial cash flow -- hence, the initial value of the contract is zero. The terminalvalue of the contract is S(T) - K. There are no other cash flows (-unlike- a future).Now consider how you would generalize this contract idea to create a forward ona path-dependent payoff like an Asian payoff, which is an average asset value overa time period. The payoff is P(T) = Sum S(t_i)/n, where t < t(1) < t(2) , ..., t(n) <= T. P(T) is the realized average value over (t,T). The agreement would be to deliver P(T) at time T > t for a fixed strike K. (times a notional if you like). The strike is chosen so there is no initial cash flow, so the initial value of the contract is zero. The terminalvalue of the contract is P(T) - K. There are no other cash flows.This same idea works for a variance swap, which is simply another path-dependent payoff.Now the payoff is P(T) = Sum [log S(t_i)/S(t_i-1)]^2/n. Thestrike K is set for no cash flow again. The terminal value is P(T) - K, where P(T)is now the realized variance over (t,T).The quick version of the above:swap = forward.