Variance Swaps Offer More Stable Volatility Exposure Than Single Options
Summary
The document compares variance swaps with options for expressing a view on volatility. Its central point is that a variance swap's vega is described as independent of the underlying price, while the vega of a single option changes with spot and is greatest around a particular price relative to the strike. A variance swap can therefore offer a more direct sensitivity when the intended exposure is volatility rather than direction in the underlying.
A portfolio of options across multiple strikes can approximate this exposure, and the response connects that construction to theoretical variance swap valuation. Operationally, a single swap may be simpler than managing many options. The trade-off is market access: the document characterizes variance swaps as over-the-counter contracts traded by a limited set of dealers, with less publicly available pricing and market data than listed index options. These points are qualitative; actual liquidity, pricing, contract terms, and exposure can vary by market and product.
Key ideas
- A variance swap is presented as having vega that does not vary with the underlying price.
- A single option's vega depends on spot and is concentrated around prices near its strike.
- A portfolio of options at multiple strikes can provide broader volatility exposure and underlies variance swap valuation logic.
- Over-the-counter access and limited public market data can make variance swaps less practical than listed alternatives.
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Full text
# Why would one prefer variance swaps over other instruments?
# Why would one prefer variance swaps over other instruments?
I understand that an investor who has a view on an underlying's variance would be tempted by a variance swap. But why would one prefer such a contract over another instrument whose value is based on volatility, eg. options ?
## Answer by Alex C (score 3, accepted)
https://quant.stackexchange.com/a/27581
Clearly, from a theoretical point of view, a varswap is a better way of capturing volatility change, since as mentioned by Mark Joshi a varswap has, by construction, a Vega that does not vary with the stock price. For a single option on the other hand the Vega is at maximum at a stock price $S^*$ roughly comparable to the strike price X and decays in a "bell shaped" fashion for stock price higher or lower than this. (The modal Vega stock price is $S^*=X\exp((-r-\frac{\sigma^2}{2})T$), "below but close to X", as Mario Draghi would say).
When you are betting on volatility and not on the stock price you would clearly prefer to have a fixed Vega (i.e. a fixed sensitivity to vol), unaffected by stock price movement.
This could be also accomplished by having a portfolio of options of various strikes, some above and some below the current stock price, so you have all bases covered if the stock price starts to move up or down between now and maturity. And, amazingly enough, it is by analyzing this strategy that theoreticians have come up with the formulas for valuing varswaps. It is the same logic.
From a practical point of view buying a static portfolio of many options is more difficult to deal with than buying a single varswap. The varswap is more convenient.
But from a practical point of view the varswap also has a disadvantage. The varswaps are OTC instruments traded by a few major IBs only. (Unlike the CBOE traded index options). The prices of varswaps are not published in the WSJ or anywhere else, and as far as I know there has been no academic study of the varswap market pricing, liquidity, efficiency, etc. because the research data is not available. Until then therefore, I will personally stick with index options and VIX futures when I trade volatility.
## Answer by Mark Joshi (score 5)
https://quant.stackexchange.com/a/27575
The vega of an option is very dependent on the spot price. The vega of a variance or volatility swap is not.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.