What is the term structure of volatility and how does it affect options risk management?

The term structure of volatility describes how implied volatility varies across different expiration dates for options at the same strike (typically ATM). Combined with the smile/skew across strikes, it forms the full volatility surface.

Common Shapes

1. Upward Sloping (Contango): Short-term vol < long-term vol. This is the "normal" state — uncertainty compounds over time.

• Example: 1-month ATM vol = 16%, 6-month = 19%, 1-year = 21%

1. Downward Sloping (Backwardation): Short-term vol > long-term vol. Occurs during market crises when near-term uncertainty spikes.

• Example: 1-month ATM vol = 35%, 6-month = 25%, 1-year = 22%

1. Humped: Vol peaks at an intermediate maturity, then declines. Often seen around known events (elections, central bank meetings, earnings).

Why Does the Shape Change?

• Mean reversion of volatility: Volatility tends to revert to a long-run average. During crises, short-term vol spikes but long-term vol rises less because markets expect the crisis to pass.
• Event risk: Known upcoming events (e.g., an election in 3 months) push up vol around that tenor.
• Supply/demand: Structured product issuers systematically sell long-dated vol (autocallable notes), suppressing long-end vol.

Impact on Vega Risk

A position's vega exposure depends on which part of the term structure it's exposed to. Consider two portfolios:

If the term structure steepens (short vol rises, long vol stable), Fund A loses money while Fund B is unaffected. This is why a single portfolio vega number is misleading — you need vega bucketed by tenor.

The Full Volatility Surface

The complete picture combines strike and tenor dimensions:

Risk managers must monitor the entire surface, not just a single implied vol number. Changes in the surface shape — parallel shifts, steepening/flattening, and smile widening/narrowing — each create different P&L impacts.

Example: Bancroft Options Trading holds a book of equity index options across maturities. Their risk report breaks vega into tenor buckets: -$50K/vol point at 1-month, +$20K at 3-month, +$80K at 1-year. The net vega is +$50K, but a term structure flattening (short vol up, long vol down) would lose money despite the net long vega position.

For the FRM exam, understand the shapes, the economic drivers, and why bucketed vega is superior to aggregate vega. Practice with our FRM volatility materials.