Put Options Are Not Too Expensive— An Analysis of Path Peso Problems —

The observed prices of out-of-the money put options seem too high given standardderivative pricing models. One possible explanation is a Peso problem: crashes (forwhich the payoff of a put is high) are taken into account for pricing, but are under-represented in the data sets used for empirical tests. This explanation is rejected byBondarenko (2003b) who shows that his newly derived pricing restriction controllingfor the peso problem is violated.In this paper, we argue that the approach presented by Bondarenko (2003b) onlysolves the problem of missing terminal stock prices (’state peso problem’), but thatthe problem of missing paths for the price of the underlying (’path peso problem’)remains. We derive analytical expressions for the effect of the path peso problemon the new pricing restriction, and we show under which conditions a correctlypriced claim appears overpriced or underpriced in an empirical test. The potentialmagnitude of the path peso problem is analyzed in a simulation study. We arguethat the results of existing empirical studies can be explained by the path pesoproblem, so that the high prices of put options do not necessarily reject standardasset pricing models.