Volatility
Table of Contents
1. Summary
Volatility is one word for two different things, and most confusion in this cluster comes from sliding between them. Realised volatility is a statistic: the dispersion of returns actually observed. Implied volatility is a price: the number that makes a pricing model reproduce a quoted option premium. The first is measured from history, the second is backed out of the market, and they agree only by coincidence.
The cluster follows that split and then its consequences. Once implied volatility is understood as a price, it has a term structure and a strike structure — a surface — which must obey constraints or it admits arbitrage, which moves in a particular way when spot moves, and which can itself be traded. Read in that order: the concept, the surface, the constraints on the surface, its dynamics, and finally the instruments.
2. Reading order
2.1. The concept
Volatility — start here. Dispersion of returns, standard deviation, annualisation, and the realised-versus-implied distinction the rest of the cluster depends on.
GARCH Volatility Models — read second, while still on realised volatility. Volatility clusters rather than arriving independently each day, and GARCH is the standard way to model that. Read it here rather than later for one specific connection: the leverage asymmetry a GJR-GARCH captures produces qualitatively the same negative skew the surface shows, which makes the surface's shape legible when you meet it.
Do not carry that further than it goes. Realised volatility is a time-series property under the real-world measure; the surface's shape across strike is a risk-neutral pricing phenomenon driven by the pricing density, jumps and tail risk. The two rhyme at the leverage effect and are not the same claim.
2.2. The surface
FX Volatility Surface — the structure, construction and conventions: pillars in expiry and in delta, and the quoting conventions that make FX different from equities. This is the cluster's centre of gravity; everything after it is either a constraint on the surface or a consequence of it.
2.3. What the surface must satisfy
Vol Surface No-Arbitrage Conditions — what arbitrage means for a surface and the conditions one must satisfy to be free of it. Read directly after the surface: these are the constraints any interpolation or fitting has to respect, and a surface that violates them prices a free lunch.
2.4. How the surface moves
Skew Stickiness Ratio — sticky strike against sticky delta, and what happens to the smile when spot moves. This is a dynamics question and only arises once the static shape is settled.
FX Vol Surface Driving — the driver and derived pattern applied to surfaces, for the case where one surface is generated deterministically from another rather than quoted in its own right.
2.5. What is traded on it
Variance and Volatility Derivatives — variance and volatility swaps and options, with barriers, corridors and baskets. Last in the sequence because these instruments take the surface as an input: they are priced off it rather than contributing to it.
2.6. The papers, when the question is method
Two research notes sit alongside rather than in the sequence. Reach for them when the question is how to do something rather than what it is.
- Arbitrage-free surface interpolation — interpolating a surface without violating the conditions above.
- GJR-GARCH and neural option pricing — combining the realised-volatility model with a learned pricer.
3. What this cluster does not cover
Interest rate curves are the other term structure and have their own structure note. They share the pillar-and-interpolation machinery, so the vocabulary carries over, but nothing else does: a curve discounts and a surface prices optionality.
4. See also
- Knowledge — the index this structure note hangs from.
- Interest Rate Curves — the sibling term-structure cluster.
- Zettelkasten — what a structure note is and why the order is authored rather than computed.