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Why do two different products trades as vol swap and var swap. Are these products not inter-convertible? I know Var swap has convexity and vol swap does not have but i don not understand how it helps in risk management. Can we calculate Vol of Vol if we know about vol swap and var swap? Is there any product like vol-var swap, i have seen this term being used?

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At the begining, there were only variance swaps who were traded for vega hedge purpose or to speculate directly on the volatility. They were famous products thanks to the formula that links the variance to european call and put prices.

As for volatility swaps, they appeared because of the convexity of variance swaps but they are more complex to price. A common method is to price them using Heston model and Fourrier transform in order to get the expected value of volatility as function of heston parameters.

The vol of vol means the the volatility of a vol index like VIX which is a measure of expected implied volatility for S&P 500 options.

Now, there are many volatilty products that appeared like variance options, volatility options and so on.

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  • $\begingroup$ You said the volatility swap appeared because of the convexity (with volatility, right?) of variance swap. Could you elaborate more, for example, what is the problem if the market has only products which are convexe with volatility? $\endgroup$
    – NN2
    Mar 4, 2021 at 0:38

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