Interactive · bilinear interpolation over the simulated 3×3 surface
Hedge sizing console
Set price volatility and forecast error, then read the hedge ratio, objective curve, risk statistics, and benchmark savings from the Monte Carlo surface.
Horizon
180d
Paths
12k
Budget
$9.49M
Scenario presets
quick jumps, sliders stay authoritative
Objective curve
J(h) at current conditions
σ 25.0% · cv 0.168
h*
0.95
High-cover interior
J(h*)
$501k
5.28% of budget
E[N]
$211k
expected net cost
CVaR95
$982k
worst 5% mean
Benchmark delta
objective saved, % of $9.49M budget
No hedge
h = 0
3.27%
Half hedge
h = 0.5
1.94%
Full hedge
h = 1
0.08%
Drag volatility up and the trough moves right. Drag forecast error up and it moves left. The optimizer is doing both at once, which is the part a static rule cannot see.
Inside the objective
Five costs, one hedge ratio
Each Monte Carlo path prices the same terms, then minimizes E[N] + σ[N] over h.
(F − P_lock) · min(D, Q_h)Premium on used cover
The certain price of insurance: forwards cost 1.5% over the locked price, paid on every hedged unit customers actually redeem.
Σ (S_t − P_lock) · U_tUnhedged spot exposure
Redemptions beyond the hedge are bought at spot and delivered at the stale locked price. This is the term that explodes when prices rise.
(F − S_T) · LClose-out of unused cover
Cover the customers never claimed becomes a speculative position, unwound at whatever the price happens to be. Loses exactly when demand came in low and prices fell.
λ·m·F·Q_h · T/252Capital cost of margin
10% initial margin financed at an 8% annual opportunity cost for the life of the hedge.
π · max_t Φ_tLiquidity spike penalty
Cash committed to the hedge is cash unavailable when a redemption spike hits: peak shortfall is penalized at the cost of forced short-term funding.
Parameters: forward premium 1.5% · initial margin 10% · capital cost 8%/yr · liquidity penalty 2% of peak shortfall · cash buffer 10% of expected demand value · horizon 180 trading days. Full derivation in §4 of the paper.