Defining volatility 5

Taking vol positions by using straddles/strangles 5

Taking vol positions by delta-hedging options 6

The emergence of variance swaps and their valuation 8

The variance swap mechanism 8

Pricing: the intuitive approach 10

Pricing: Carr and Madan’s formal approach 11

Why not volatility swaps? 13

Characteristics of volatility 14

The behavior of variance swap strike prices 15

Variance swap strike prices as a forecast of future realized volatility 16

The variance risk premium 17

Why use variance swaps? 19

Implied/realized volatility arbitrage 19

Volatility pairs and dispersion trading 20

Hedging structured products 22

Immunizing volatility risk of hedge fund strategies 23

Third-generation volatility products 24

Gamma swaps 24

Orderly dispersion trading 26

Forward-start variance swaps 26

Corridor variance swaps 27

Up and down corridor variance swaps 27

Up and down conditional variance swaps 29

Riding the smile 29

Correlation trading 31

Conclusion 34

Appendix 35

Hedging options when volatility is unknown 35

Valuing gamma swaps 36

The Derman et al. replication of variance swaps and its extension to gamma

swaps 38

swaps 38

Example of capped variance-swap termsheet 40

References and further reading 42