We know that the volatility is lower when the sampling period is longer, for example $\sigma_{7days} < \sigma_{1day}$, Then I came across this strategy that I cannot quite understand how to exploit this:

It says: If weekly historical vol < daily historical vol:
buy strip of T options, delta hedge daily;
sell strip of T options, delta hedge weekly.

Adding up:

We do not buy nor sell any option;
play intra-week mean reversion until T;

Daily Vol / weekly Vol Arbitrage: On each leg: always keep $a invested in the index and update every Δt;

Resulting spot strategy: follow each week a mean reverting strategy;

Prove that we should keep each day the following exposure: $$ a.(\frac{1}{S_{t_{i,j}}} - \frac{1}{S_{t_{i,1}}})$$ where $t_{i,j}$ is the j-th day of the i-th week

It amounts to follow an intra-week mean reversion strategy

Could someone helps to explain a little?

  • $\begingroup$ Bruno Dupire is the author of this strategy. $\endgroup$
    – Alex C
    Feb 25 '18 at 22:02
  • $\begingroup$ yes! but I don't quite understand @Alex C $\endgroup$
    – Qing
    Feb 25 '18 at 22:04

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