Volatility Investing Handbook
BNP Paribas 2005

Variance swaps and beyond





Table of contents
Executive summary 3
Volatility investing: an old story with some recent innovations 4
Volatility investing: the traditional way 5
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
Example of capped variance-swap termsheet 40
References and further reading 42