## Eurex exchange – colin bennett on volatility trading. part 2 volatility futures as an alternative to equity and puts equity meaning in economics

Returns over relatively short periods of time hide the fact that volatility is floored at a certain level, for example the VSTOXX® never trades below c12%. This means that the loss from a long VSTOXX® Future is floored, hence returns over a longer time period (e.g. 3 months) show a more convex profile than daily returns usd today. A long Volatility Future can therefore be compared against puts, particularly when volatility is low and the impact of the volatility floor is greatest.

As a Volatility Future is a future on a 1 month Volatility Index, the implied volatility of a 3 month Volatility Future trades in line with that of a 4 month put. The return of Volatility Future of 3 month expiry until maturity should therefore be compared to the 3 month return of a 4 month put (i.e. the return of a put with 4 month maturity up until it has only 1 month left to expiry).

Similarly, the return of a Volatility Future with 1 month until expiry should be compared to the 1 month return of a 2 month put (i.e. return of a put with 2 month maturity until it has only 1 month left to expiry). For both 3 month Volatility Futures (vs 4 month ATM put) and 1 month Volatility Futures (vs 2 month ATM put) the payout of an ATM put is very similar to the payout of 5 VSTOXX® Volatility Futures hkd __usd exchange rate__. Hence 5 VSTOXX® Volatility Futures could be considered an alternative to one SX5E ATM put. It should be remembered that the payout of a Volatility Future is less reliable than that of a put.

While having a non-standard expiry could be seen to be confusing, it does mean that on the date of expiration, the underlying Volatility Index is calculated using the implied volatility for only one maturity (no interpolation or extrapolation between two expiries is needed). A Volatility Futures that expires in November, will therefore be hedged by trading a strip of options for the December expiry one month later.

When an unexpected event occurs, volatility normally jumps. As markets digest the news, volatility tends to soften and mean revert over a period of up to 10 months **binary translator google**. This mean reversion can be seen by plotting the minimum and maximum implied volatility per maturity (a volatility cone) as can be seen in the chart below. As near dated implieds have a wider min-max range than far dated implieds, this means that when a volatility index spikes near dated Volatility Futures rise more than far dated volatility futures. Far dated Volatility Futures could be seen as a more stable (or less levered) way of gaining volatility exposure.

Volatility tends to jump, and then mean revert over a period of time just under 1 year. Near dated Volatility Futures will therefore have a delta (or exposure/sensitivity) to the underlying Volatility Index of nearly 100% (e.g. c90% for 1 month volatility futures). The delta (or exposure/sensitivity) of Volatility Futures will fall as maturity increases, as mean reversion makes it unlikely that the current levels of volatility will remain over the entire life of the Volatility Futures. A plot of the sensitivity (i.e. delta) of Volatility Futures to the underlying Volatility Index is shown above both for rolling every month, and for rolling at expiry. For example, the 3 month data point can either always have a 3 month maturity (i.e. it is rolled when the maturity reduces to 2 months) or can have a maturity between 0 and 3 months (i.e. it is rolled at expiry) *equity meaning* in urdu. The delta when rolling at expiration can be considered a blend of the deltas when 1 month rolling. For example, the delta of a 3 month future rolled at expiry is a blend of the deltas of the 3, 2 and 1 month future rolled after 1 month.

The diagram above shows the delta of a Volatility Futures rolled at expiry vs the number of times in a year you have to roll the position. Investors seeking the highest delta should always use 1 month futures and roll 12 times per year us futures exchanges. Investors seeking a balance between the delta, and the overhead of rolling the position should use 3 month futures and roll at expiry (i.e. roll 4 times a year). While using 2 month futures has a higher delta than 3 month futures, it is not very significantly for the additional overhead of rolling 6 times a year rather than 4. Using 4 month futures only saves 1 roll per year (as you roll 3 times not 4) and has a significantly reduced delta compared to 3 month futures.

In addition to considering the sensitivity of a Volatility Futures to the underlying index, and the number of times the position has to be rolled, and investor should also consider how expensive the position is to hold shoe size conversion uk to us. As term structure is on average upward sloping, this means a Volatility Futures should on average decline as maturity approaches. As the slope of term structure is relatively flat at the far end, longer dated Volatility Futures suffer less from time decay than near dated Volatility Futures. This can be seen in the diagram below. To reduce the impact of time decay an investor can use far dated futures, potentially rolling when the position is 2 months or less usd to nzd exchange rate history. This strategy would have a lower delta than using near dated futures. There is in effect a trade-off between the cost of holding the position, and the effectiveness of the position. Should an investor be using Volatility Futures tactically (i.e. not all the time, but only in advance of key events likely to cause high volatility) near dated Volatility Futures are likely to be preferred. If an investor is using volatility strategically (i.e. continuously as part of a diversified portfolio) far dated Volatility Futures (potentially rolled before expiry) is likely to be preferred.

A Volatility Futures will be hedged with a strip of options of all strikes. As OTM options are typically less liquid than ATM options, Volatility Index providers have rules to exclude OTM options if they are too far OTM or are illiquid british pound to dollar exchange rate. While this improves the reliability of the Volatility Index calculation, it makes it harder for traders to hedge as they are not certain if they need to trade an OTM option or not (a sudden change in spot or liquidity approaching expiry could cause the option to be included or excluded from the calculation). In deciding the methodology, there is a trade-off between how easy it is for liquidity providers (i.e. market makers and traders) to hedge and data reliability. Typically end clients are reluctant to trade an instrument that could expire at a significantly different value to the prints just before and just after expiration. Just as there have been issues with the settlement price of equity indexes (e.g. the FTSE June 2005 expiration) there can be issues with the settlement price of Volatility Futures.

Despite the fact Volatility Futures use a variance swap based calculation, the fair price of a Volatility Futures is not equal to forward variance **gender differences**. In fact the fair price of a volatility future is below that of forward variance. As maturity (and volatility of volatility) increases the difference between the price of a variance swap and Volatility Futures widens. This can be seen by comparing a Volatility Index such as the VSTOXX® with a forward variance swap. We note that volatility of volatility can be seen in an index such as the VV2X, which is the volatility of options on VSTOXX® Futures.

Volatility Futures tend to trade just below the levels of forward variance. If a Volatility Futures traded at the same level as forward variance an arbitrageur could simply go long forward variance and short Volatility Futures to construct a portfolio that can only earn profits. This can be seen by looking at the pay-out of a VSTOXX® Volatility Futures and a forward 30 day (to match VSTOXX®) variance swap for identical vega. We shall assume the strike of both the VSTOXX® and forward variance is 20. As vega gives the P&L sensitivity to volatility, having identical vega means the pay-out should be identical for small deviations of volatility about the level 20 (i.e. the gradient of the two lines are identical for volatility at 20). The diagram below shows the pay-out of forward variance is always equal to or above the pay-out of the VSTOXX® (if they are the same price), hence a long forward variance short VSTOXX® portfolio only has a positive pay-out.

Typically Volatility Futures are expensive, which is why many trading desks put on a short Volatility Futures long forward variance position **love quotes**. As a short Volatility Futures position is long volatility of volatility, this means a short Volatility Futures long forward variance position is also long volatility of volatility (an uncapped variance swap has zero volatility of volatility exposure). The value from this position can be extracted by selling (a strip of) options on Volatility Futures, as options on Volatility Futures (like most options) are on average expensive.

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