Volatility Surface Dynamics

Knowing today's volatility surface is not enough to manage options risk. You also need to know how the surface will change when the underlying price moves and when volatility shocks hit. These "surface dynamics" determine how option prices respond to market moves beyond what delta and vega alone predict, and they determine the right hedge ratio. Different assumptions about dynamics can change the delta of an option position noticeably, which is why traders and models argue about them.

The core question#

If the stock moves from $100 to $95, what happens to the implied volatility of the $100 strike option? The answer depends on the regime and the market.

See Volatility Smile and Skew and Local Volatility.

Why it matters for delta#

The true sensitivity of an option to the underlying includes the effect of changing implied volatility:

effective delta ≈ model delta + vega × (change in IV for a $1 move)

Spot vol correlation#

For equity indices, implied volatility usually rises when prices fall and falls when prices rise. This negative spot vol correlation is captured in models through:

• Negative ρ in stochastic volatility models such as Heston. See Stochastic Volatility and the Heston Model.
• Skew dynamics in local volatility.
• The backbone and ρ in SABR. See SABR Model.

The strength of this relationship varies. In sharp selloffs, implied volatility can jump far more than the skew predicted ("vol up, spot down" on steroids); in slow grinding declines, it may barely move.

Regimes#

Researchers and traders, including Emanuel Derman, have described regimes in which different dynamics hold:

Term structure dynamics#

Short dated volatility moves more than long dated volatility, often roughly in proportion to one over the square root of time. A common rule of thumb weights vega by √(reference time / option time) to compare exposures across expiries. See Volatility Term Structure.

Forward smiles#

Some products depend on what the smile will look like in the future, such as forward starting options and cliquets. Local volatility tends to predict that future smiles flatten; stochastic volatility models keep them steeper, closer to what markets show. This is a key reason banks use stochastic or local stochastic volatility models for such products.

Practical implications#

• Hedge ratios: adjust deltas for expected volatility changes, especially for index options.
• Risk reports: include scenarios where volatility moves with price according to historical spot vol relationships. See Stress Testing and Scenario Analysis.
• Strategy choice: short put positions lose twice in selloffs, from price and from volatility; long puts gain twice.
• Model choice: pick models whose dynamics match the products and markets traded.

Common mistakes#

• Using pure model delta for index options without considering skew dynamics.
• Assuming one regime always holds.
• Ignoring that short dated volatility moves most.

Frequently asked questions#

What is sticky strike?#

The assumption that each strike keeps its implied volatility when the underlying moves, so at the money volatility changes as price moves along the skew.

What is sticky delta?#

The assumption that implied volatility at each moneyness or delta stays the same, so the whole smile moves with the underlying price.

Why do surface dynamics affect hedging?#

Because implied volatility changes as the price moves, and that change alters option values, so the effective delta differs from the model delta.

Next, learn how to trade volatility itself in Volatility Trading.