# 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.

• Are you sure the option has a maturity of 30 days? On 31 January 1996 the next maturity dates are 16 Feb 1996 or 15 Mar 1996 (assuming these are monthly SP500 options on the regular calendar, third friday of the month). These would be 16 or 44 days in the future (unfortunately neither of which gives your desired result, where did you get 589.95 ? ). – noob2 Feb 18 at 19:08
• Apologies, the holding period is supposed to be 30 days. So the option is written on 31 Jan 1996, repurchased on 29 Feb 1996. Effectively having a holding period of 29 days. The maturity, however, is 45 days, namely the 16 Mar, where the feasible strike is $590$. The selection rule is such that the strike should be below the calculated strike, and the maturity date should be after the roll date (30 days). – Mkl Feb 19 at 8:03