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Statistik › Optionen, Shorts und Positionierung › Index put premium

The famous index put premium is not statistically significant

0.94 moneyness
-56.8%
0.96 moneyness
-52.3%
0.98 moneyness
-44.7%
1.00 moneyness
-29.9%
1.02 moneyness
-19.0%

Average monthly return to BUYING S&P 500 futures puts, August 1987 to June 2005, 215 months. t statistics run from minus 3.3 to minus 4.2. Writing the puts earns the opposite sign. The pattern is clean, monotonic and, for the deepest strikes, not statistically distinguishable from a model with no mispricing in it.

Buying out-of-the-money S&P 500 puts lost 56.8% a month for eighteen years, a figure quoted everywhere as proof that crash insurance is overpriced. Under a finite-sample test the same number has a p value of 8.1% and does not reject.

-56.8%Monthly return to buying the 0.94 moneyness S&P 500 put, 1987 to 2005
8.1%Finite-sample p value of that figure against Black-Scholes
24.1%The same p value against a stochastic volatility model
-15.7%Monthly return to at-the-money straddles, which does survive the test

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