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In the Discrete Stochastic Implied Volatility Model which is from the standard Heston Model, the model shows the evolution of forward implied volatilities with time.

I thought forward implied volatility for each time step is not the same as the instantaneous volatility of each time step.

Am I right?

For your reference, I attached the paper below.

http://www1.maths.ox.ac.uk/system/files/legacy/12804/StochasticImpliedVolatility.pdf

Thanks in advance.

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