In this paper, we describe a method of replication for variance swaps using a clever decomposition of the log-payoff and a basket of options that bypasses the path-dependent property of a delta-hedged option. From our knowledge, the proposed approach to the fair value of future variance is the most rigorous from a theoretical point of view, and makes less assumption than the intuitive treatment generally proposed. The intuitive approach behind the replication of variance swap relies on building empirically a portfolio whose variance sensitivity becomes independent of the stock price based on the observation that the net P&L (profit/loss) of a delta-hedged option exhibits a curvature varying sharply as stock prices move. An attractive feature of the presented method is that the future volatility indicated in the diffusion process (i.e. the so-called local volatility model) does not provide insight into how to replicate the fair strike. Therefore, no explicit stochastic model for volatility is required to perform the replication. The essence of the replication is to devise a position that, over the next instant of time, generates a payoff proportional to the incremental variation of the stock during that time. Our approach differs from other publications since we specify, step-by-step, how to find a portfolio that replicates a variance swap at all future stock price levels using a rigorous theory. In general, this requires an infinite number of options for an exact replication. We can then use the same method with only a limited number of options to replicate the variance swap exactly at a limited number of stock prices. By increasing the number of options in the replicating portfolio, we can increase the accuracy of the replication. While efficient, denote that the approach does not allow to compute the Greeks and assumes the sample mean in the definition of realized variance to be zero in order to make possible the derivation of the replicating strategy. In a similar way as performed in the Black-Scholes option pricing framework, the modeling approach assumes a continuous diffusion process for the underlyer and does not allow for jumps. The conditions under which the replication strategy holds, and the correct answers when they do not hold, are clearly noticed in this paper. The limitations of the replicating approach are also discussed.