{"categories":["Risk Management"],"contentHtml":"<p>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.</p>\n<p>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.</p>\n<p>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.</p>","contentMarkdown":"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.\n\nThe 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.\n\nThat 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.","dataUrl":"https://sharifhsn.dev/api/posts/options-and-volatility.json","date":"2024-12-12","datePublished":"2024-12-12","description":"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 …","site":"https://sharifhsn.dev","slug":"options-and-volatility","source":"FE-535 | Risk Management","sourceUrl":null,"tags":["Risk Management","Options","Volatility"],"title":"Options and Volatility","url":"https://sharifhsn.dev/blog/options-and-volatility/","version":"1","wordCount":117}