Choosing S&P 500 Put Strikes with Implied-Volatility Z-Scores

Summary

The document describes a monthly index put-writing strategy attributed to Jurek and Stafford. It selects option strikes using a volatility-scaled Z-score rather than a fixed strike-to-spot ratio. The stated relationship combines the index level, next-month implied volatility, and the chosen Z-score to set the strike. Premium proceeds are invested at the risk-free rate.

The author checks the method with a historical example using an index level, implied volatility, and a two-standard-deviation downside level. Their calculation differs from the example because they scale annualized volatility by the square root of the fraction of a year in thirty days. The document does not resolve the discrepancy or establish which day-count convention the paper uses, so it serves mainly as a question about implementing the formula. It gives no strategy performance evidence, detailed option-selection rules, or risk analysis.

Key ideas

• The described put-writing strategy resets its index option position monthly.
• Strike selection uses a volatility-scaled Z-score instead of a fixed strike-to-spot ratio.
• The example’s strike differs from the author’s result after scaling volatility to a thirty-day period.
• The document leaves the appropriate time scaling and source of the discrepancy unresolved.

Tags

# Selecting strike prices for put-writing strategy based on Z-scores


# Selecting strike prices for put-writing strategy based on Z-scores












I'm trying to replicate the put-writing strategy of Jurek and Stafford from 2015 (The Cost of Capital for Alternative Investments, Jrl. Fin. SSRN). Their strategy writes index put options on the SP500, rebalancing each month and invest the proceeds at the risk-free rate.

They select strike prices based on Z-scores, not moneyness as measured by Strike/Spot-ratio. Their formula is as follows: $K(Z) = S_t * exp(\sigma_{t+1}*Z)$ , where $\sigma_{t+1}$ is the 30-day implied volatility, measured by the VIX.

My problem is that I don't get similar results as an example I've seen, based on this paper.

Example uses $S_t = 636 $ per 31. January 1996, $ \sigma_{t+1}=12.5\%$, and $Z=-2$. Then, $K(Z)=\$589.95$. However, I'm not able to get the same result, as I get $ K(Z) = 636*exp(0.125*\sqrt{30/365}*-2) = 592$. I've tried using 252 days in a year as well, without results.

Hopefully, someone here can point me in the right direction.

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