Implicit in industry standard option pricing models is the expectation that roughly 25% of stocks with 60% consistent volatility will septuple within 10 years, an extraordinary rate of appreciation. The exceptionally high equilibrium anticipated returns for an improbably large percentage of high...

Pushing models to extremes can expose output biases that stem from underlying assumptions. In the case of industry standard option valuation models, long term, high volatility securities provide a stress test vehicle. For instance, in evaluating a stock with 60% volatility, industry standard...