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Volatility Investing Handbook
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!ˉs formal approach 1
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
Equities & Derivatives Research
2
Equity Derivatives Technical Study
28 September 2005
Executive summary
The goal of this paper is to introduce investors to sophisticated derivatives
instruments that allow them to take views on volatility. Despite the fact that
volatility-sensitive derivatives have been traded for years if not centuries, it is
only recently that products giving pure exposure to volatility have appeared.
We start our overview by discussing the weaknesses of !°traditional!± methods o
volatility investing. Although buying/selling straddles is an easy way to bet on
volatility, the delta ¨C i.e. the portfolio!ˉs sensitivity to stock returns ¨C ceases to
null once the stock moves away from its initial value.
One way to circumvent this problem is to delta-hedge the positions. However,
as we shall demonstrate below, delta-hedging options does not yield pure
exposure to volatility since the trader/investor then faces a further vega risk as
well as a model/path dependency risk.
Variance swaps provide a pure view on volatility since they pay the difference
between future realized variance and a pre-defined strike price. The rapid
development of variance swaps reflects the simplicity with which they can be
valued: under certain non-restrictive assumptions, the variance swap strike
price can be shown to be equal to the value of an options portfolio that uses a
continuum of strike prices and is inversely weighted by the square of the
options!ˉ strike prices.
Variance swaps can be used in many ways, ranging from arbitraging realized
vs. implied volatility and dispersion trading, to hedging structured products or
hedge fund strategies.
We also describe other volatility products that have been developed in recent
years. Gamma swaps are similar to variance swaps but with a notional that is a
function of the asset price. They have several advantages over variance swaps
since they do not require any caps and are a more efficient tool for dispersion
trading. Finally, we present derivatives instruments such as conditional variance
swaps or corridor variance swaps that allow investors to make asymmetric bets
on volatility and take positions on the skew and the smile.
[此贴子已经被作者于2008-6-7 14:48:18编辑过]
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