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- Variance Swaps and Option Volatilities
Variance Swaps and Option Volatilities
Variance swap strikes are well correlated with BS IV derived from options prices.
--> not surprising --> both can be interpreted as market estimates of future volatility.
Similar but different:
- ATM IV reflects the market estimate of future volatility realised around the current level.
- VS represents the market estimate of variance, independent of future market level.
The table below shows ATM volatility and variance swap levels for a number of European stocks and indices.
Whilst all VS price > ATM volatility --> variation in the spread --> partly due to the differing skews.
This spread becomes larger and more unpredictable at longer maturities --> effect shape of skew becomes more important.
At 6m maturity, index variance appears rich in comparison to its ATM IV --> index having higher put skews than single-stocks.
At 3y maturity, they seem more in line --> greater upside convexity of single-stocks becomes more important.
Why does VS invariably trade above ATM IV of the corresponding maturity?
- Convexity premium: gain more from increase in volatility than corresponding loss from decrease in volatility.
- Theoretical price of VS is calculated from prices of a replicating ptf of options.
With skew and skew convexity, average volatilities will usually be above ATM volatility, making the VS more expensive.
Ultimately it comes down to the fact that a long VS is also long vol of vol, due to the convex nature of the payoff.
Convex payoff is paid through a replicating ptf of options across the skew surface, which in effect price in this vol of vol.
For short dates:
- skew relatively linear around ATM volatility
- put skews more significant than call skews
--> the price can be thought of as a function of ATM volatility level and the slop of the skew.
In practice, contribution of skew component means that VS strikes tend to trade a similar levels to OTM puts.
- 95-100 strikes for maturities of around 1-3 months
- 90-95 strikes for maturities of about a year
Skew and convexity become more important factors at longer dates --> probability of reaching more OTM strikes increases.