Are correlation swaps sensitive to stochastic volatility? Can you please justify from a theoretical point of view?
I guess you ask if there is a difference if you model them via stochastic vol as opposed to local vol for example? If so, yes. The effect is called decorrelation. Since SV has vols fluctuate as opposed to deterministic, you get more variation in the price of the underlyings. Hence, your effective realized correlation is smaller in SV.