Rough volatility · teaching module · Layer 2 — execution (Q3)

Does it give you
a trading edge?

To unwind a large position you trade it out over time — too fast and you pay market impact, too slow and you're exposed to price swings. The classical optimum for that trade-off is Almgren–Chriss. Rough volatility has memory, so maybe you can time your selling to the vol and beat it. Turn up the vol-reactivity below and watch.

Start here — a two-minute guided tour

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01 · the benchmark

Almgren–Chriss is the bar

The horizontal teal line is the Almgren–Chriss optimum — the schedule that best trades impact cost against timing risk. Anything above the line beats it; anything below is worse. The line is the bar.

02 · add vol-timing

React to the volatility

θ makes the schedule speed up when vol is high (θ > 0) or slow down (θ < 0). Slide it away from zero and the curve drops below the line — the vol-timing makes execution worse, not better.

03 · no edge

Nothing beats the optimum

Every θ lands below Almgren–Chriss — about 5 s.e. worse at the tested strength, with no edge that grows as the market gets rougher. Rough structure buys nothing at the desk. And beware the look-ahead trap — flip it on, then read the Advanced panel.

Can you beat Almgren–Chriss? θ = 1.00 · edge over AC = −5.0 s.e.
θ · vol-reactivity
1.00
how hard you time the vol
edge over AC
−5.0
s.e. — below 0 means worse
best policy found
θ = 0 (= AC)
vol-timing never helps
roughness → risk
0.95×
barely moves total risk
Vol-timing lands below Almgren–Chriss — worse, not better. Roughness gives no execution edge.
Set the vol-reactivity
1.00θ
— trade faster when volatility is high
−2 · slower in high vol+2 · faster in high vol
−2
−1
0 · AC
1
2
👁let the policy see the future: off
Flip that on and it suddenly “beats” AC — a tempting +1.52 edge. It's fake. The Advanced panel shows how it was caught.

Advanced — the edge that wasn't

THE FINDING show ▼
Almgren–Chriss execution over the rough-Bergomi engine (D24–D26): the matched-risk gap, the look-ahead artifact, the committed kill-switch bar · edge-vs-θ curve illustrative, the −0.025 gap / per-seed / 0.7% / 0.95× are the project’s measured values · runs in your browser