The value of digital options (both European and American types) can have an inverse-U shape relationship with the volatility of the underlying process! This seemingly counterintuitive proposition is driven by a particular feature of Maringale processes bounded from below (including both the...

We examine the incremental power of a large set of key fundamental, financial, and macroeconomic variables for forecasting the volatility of natural gas futures prices. Among other results, we find that the option implied volatility (IV) significantly improves the performance of predictions...