Back out annualized vol from a straddle

Question

A stock trades at \80. Its at-the-money straddle expiring in 30 days costs \4. What annualized implied volatility does this straddle imply? Use the ATM approximation.

Accepted Answer

The approximation. For an at-the-money option, the Black-Scholes call is about 0.4\,S\,\sigma\sqrt{T}, so the straddle (call plus put) is roughly 	ext{Straddle} \approx 0.8\,S\,\sigma\sqrt{T}, where \sigma is the annualized volatility and T is time to expiry in years. Plug in and solve. Here T = 30/365 \approx 0.082 years, so \sqrt{T} \approx 0.287. Rearranging, \sigma \approx \frac{	ext{Straddle}}{0.8\,S\,\sqrt{T}} = \frac{4}{0.8 	imes 80 	imes 0.287} = \frac{4}{18.4} \approx 0.22. So the market implies about 22\% annualized volatility. Sanity check via the monthly move. The straddle its…

Back out annualized vol from a straddle

Your answer

More Market Making questions