Rough volatility · teaching module · Layer 3 — hedging (Q5)

Does it help you
hedge?

Sell an option and you must hedge it — trade the underlying to cancel the risk. Under transaction costs the textbook delta-hedge bleeds money, and modern deep hedging learns a policy that beats it. That gain is real. The only question is whether the market's roughness adds anything on top — or whether it's all just the frictions.

Start here — a two-minute guided tour

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01 · the frictions edge

Deep hedging beats delta

Under costs, both curves climb above the flat delta-hedging baseline — deep hedging clearly wins (about +1.1 in CVaR, 8/8 seeds). That's the generic Buehler effect, real and worth having.

02 · rough vs smooth

Same edge, two markets

The two curves are the same deep-hedging edge — one on a rough market (H=0.10), one on a smooth control (H=0.5, identical otherwise). They sit right on top of each other. The roughness effect is the tiny gap between them.

03 · no edge

The gap is zero

That gap is +0.06 ± 0.04 — statistically nothing (z = 1.4), and it stays nothing at every friction level. Roughness adds no hedging edge beyond frictions. Flip “undertrained” to meet the artifact that nearly said otherwise.

Is the edge frictions, or roughness? c = 0.010 · deep − delta = +1.14 · roughness increment = +0.06
deep hedging · rough vol (H=0.10) deep hedging · smooth vol (H=0.5) delta-hedging (baseline)
c · transaction cost
0.010
the friction level
deep − delta
+1.14
CVaR gain — the Buehler edge
roughness increment
+0.06
rough edge − smooth edge
roughness edge?
none · z=1.4
within the noise
Deep hedging beats delta — but rough and smooth match within noise. Roughness adds no hedging edge.
Set the transaction cost
0.010c
— the level where the contrast was measured
0 · frictionless0.05 · heavy costs
0
0.005
0.01
0.02
0.05
training budget: converged
Undertrain the policy and a +0.36 roughness “edge” appears at c = 0.02 — z = 5.6, and it survives almost every check. More training dissolves it. The Advanced panel tells that story.

Advanced — the edge that kept not being there

THE FINDING show ▼
Buehler deep hedging over the rough-Bergomi engine (D40, D43): the frictions edge, the null roughness increment, the friction sweep · CVaR-vs-c curves illustrative, the +1.14 edge / +0.06 (z=1.4) increment / +0.362→+0.033 catch are the project’s measured values · runs in your browser