A Proposed Daily Versus Weekly Volatility Arbitrage Strategy

Summary

The document asks how to interpret a proposed options strategy based on a comparison between weekly and daily historical volatility. Its stated setup buys a strip of options hedged daily and sells a corresponding strip hedged weekly, then considers whether the combined position can be expressed as a spot exposure that resets through each week. The proposed exposure depends on the difference between the reciprocal of the current spot price and the reciprocal of the spot price at the start of that week. The author interprets this as an intraweek mean reversion strategy.

The post does not provide a derivation, supporting data, backtest, or an answer establishing that the proposed equivalence is correct. It also leaves key implementation details unspecified, including option maturities and pricing, hedge rebalancing, transaction costs, and the meaning of comparing volatility measured over different sampling intervals. Thus, it is best read as a question about connecting options hedging to a spot trading rule, rather than as a validated arbitrage method. The claimed mean reversion behavior and profitability remain unproven in the material.

Key ideas

• The proposal compares weekly and daily historical volatility to motivate offsetting option positions with different hedge frequencies.
• The author suggests that the combined position may reduce to a spot exposure that resets within each week.
• The proposed exposure is tied to the difference between reciprocal spot prices at the current time and week start.
• The post does not derive the exposure or show evidence that the strategy earns a profit.
• Different sampling intervals and trading costs would need careful treatment before evaluating the proposal.

Tags

# Frequency Arbitrage


# Frequency Arbitrage












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?

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.