Variance Swaps, Volatility Swaps, and Volatility of Volatility

Summary

The document outlines why variance swaps and volatility swaps are distinct products. Variance swaps became established instruments for volatility exposure and hedging, in part because variance can be related to prices of European calls and puts. A volatility swap pays on realized volatility, while variance exposure is convex with respect to volatility; this convexity means the two payoffs are not directly interchangeable without accounting for the difference.

It notes that volatility swaps are more involved to price and describes using a Heston model with Fourier methods to estimate expected volatility. It defines volatility of volatility as the volatility of a volatility index, using VIX as an example. The response mentions variance and volatility options as related products, but it does not explain a vol-var swap, derive hedging adjustments, or provide pricing equations. Its discussion is introductory and leaves the detailed risk-management implications open.

Key ideas

• Variance swaps provide direct exposure to variance and can be linked to European option prices.
• The convex payoff relationship means a variance swap and a volatility swap are not directly interchangeable.
• Heston modeling and Fourier methods can be used to price volatility swaps.
• Volatility of volatility describes fluctuations in a volatility measure such as VIX.

Tags

# Volatility Swap Variance swap


# Volatility Swap Variance swap












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?

## Answer by Valometrics.com (score 3)

https://quant.stackexchange.com/a/51070

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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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.