Mimicking the one-dimensional marginal distributions of stochastic diffusions

In the large maturity limit, we compute explicitly the Local Volatility surface for Heston, through Dupire’s formula, with Fourier pricing of the respective derivatives of the call price. Than we verify that the prices of European call options produced by the Heston model, concide with those given by the local volatility model where the Local Volatility is computed as said above.