Options and Volatility
- Risk Management
The final FE-535 notes turn to nonlinear risk through options. An option's payoff is convex, so a small change in the underlying can have a different effect depending on where the price sits relative to the strike. Delta is the local slope; gamma measures how quickly that slope changes.
The VIX discussion is a reminder that implied volatility is a market price of uncertainty, not a direct forecast of realized volatility. Volatility can vary with strike and maturity, producing a surface rather than a single number.
That curvature is why a delta hedge must be rebalanced. A position that looks neutral for one price move can acquire substantial exposure after the underlying moves or implied volatility changes.