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...

In a discrete-time market, we study model-independent superhedging, while the semi-static superhedging portfolio consists of three parts: static positions in liquidly traded vanilla calls, static positions in other tradable, yet possibly less liquid, exotic options, and a dynamic trading...