Volatility term structure is believed to be a common phenomenon across asset classes. In equity indices, it’s well-known that implied volatility (IV) is generally greater than realized volatility (RV) (i.e. there exists a so-called volatility risk premium), and out-of-the-money (OTM) IV is greater than at-the-money (ATM) IV (i.e. there exists a so-called volatility skew). The existence of the volatility risk premium makes developing long volatility strategies a very difficult, if not impossible, task. Similarly, volatility skew makes tail risk hedging expensive.

Many studies have been carried out on the US equity indices. Little research has been devoted to international equity indices. Among few studies, Reference [1] examines the volatility structure of the DAX index. Specifically, it investigates PnLs of delta-hedged short options trading strategies. One of the simulated strategies is as follows,

*Delta-neutral hedge without transaction costs. Hedge-volatility equal to the implied volatility of an option. Options are sold at bid/ask midpoint and DAX-index is traded at the closing price of DAX 30.*

Table 19 of Reference [1] summarizes the PnL of the above strategy. From the results, we observe that,

- For Deep OTM options, their PnLs are consistent with ours,
- For OTM put options, 1-Month delta-hedged short options show negative PnL; this means that we would be able to design a cheap tail hedge,
- Results for ATM options are even more surprising. Except for 3-Month put options, all other ATM options yielded negative PnL. This means that we would be able to design long-volatility trading strategies that have positive expectancies [2].

In short, the results are quite surprising. This may be due to the followings,

- DAX volatility term structure is different from SP500’s,
- The period covered by data used in the study was not long enough. The options data covers only the 2018-2019 period.

We believe that #2 is likely the cause. It’s well-known that after the crash of February 2018, US equity indices’ RVs exceeded IVs, thus making short volatility trading strategies such as butterflies unprofitable. To make any conclusion regarding #1, more data should be used.

**References**

[1] J. Juvakka, *Profit potential of DAX index option trading based on implied volatility surfaces*, LUT School of Business and Management, 2020.

[2] Transaction costs are not accounted for.

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