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Are correlation swaps sensitive to stochastic volatility? Can you please justify from a theoretical point of view?

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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.

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  • $\begingroup$ Thanks a lot for your reply, AKdemy. The argument sounds good. But will it be a significant change as compared to the local vol is a valid question. Because stochastic vol may not necessarily increase the randomness of the underlying stock and decorrelate. We may simply need a very high value of vol for the decorrelation effect, not necessarily a stoch vol. $\endgroup$
    – ahr1729
    May 10 at 8:31
  • $\begingroup$ No matter your level of vol, LV will never decorrelate as vol is deterministic. ellie_cat added a good comment about validity of LV. I also mentioned here that LV is often actually close to market quotes. $\endgroup$
    – AKdemy
    May 10 at 9:01

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