Volatility surfaces, skew and term structure
If Black-Scholes were right, every option on the same stock would have the same implied volatility. In practice, implied volatility varies by strike and by expiry. Plot it across both and you get the volatility surface.
Skew: across strikes
In equity indices, downside puts trade at higher implied volatility than upside calls. Two reasons: crashes happen faster than rallies, and investors consistently pay up for protection. In some markets the curve is more symmetric (a smile), and in commodities like natural gas, upside calls can be the expensive side, because supply shocks spike prices.
Changes in skew carry information. Steepening skew means demand for downside protection is rising. Flattening or upside skew can signal speculative call buying.
The full surface
Put skew and term structure together and you get a surface: implied volatility for every strike and every expiry.
Term structure: across expiries
Usually longer-dated options have higher implied volatility than short-dated ones (upward-sloping, or contango). In a crisis it inverts: near-term volatility jumps above long-term, because the fear is about now. Known events also show up as bumps: an earnings date or election puts a kink in the term structure at that expiry.
The VIX
The VIX is a measure of 30-day implied volatility on the S&P 500, calculated from a strip of options. It is often called the fear index. It's mean-reverting: spikes don't last, and very low readings don't either. VIX futures have their own term structure, and in calm markets the roll from expensive futures to spot is what slowly erodes long-VIX products.
Implied vs realised
Implied volatility is what the market expects. Realised volatility is what actually happens. Historically, implied has usually been higher than realised, which is the volatility risk premium option sellers try to collect (lesson 3.3). When realised exceeds implied, option buyers win.
How the surface is used
- Pricing any option consistently with the rest of the market.
- Spotting relative value: options that look cheap or expensive versus their neighbours.
- Reading sentiment: where the fear is, and when it is expected.
Key takeaway
The vol surface is the market's map of risk across price levels and time. Its shape tells you what investors fear and when.
Educational content only, not financial advice. Investing involves risk and you can lose money.