Working paper · July 2026
Dynamic Hedge-Ratio Optimization for Stored-Value Products Under Uncertain Redemption Demand
When a company sells customers a locked-in price on a volatile good, it must hedge an exposure whose size and timing its own customers control. This paper builds the first model that sizes that hedge directly from a redemption forecast.
Figure: objective J(h), medium volatility × medium demand uncertainty (12,000 Monte Carlo paths)
The whole argument in one curve: hedge too little and spot exposure dominates; hedge too much and premium leakage plus the close-out lottery on unused cover dominate. The optimum is interior, and it moves with both price volatility and forecast quality.
The gap this closes
Institutional hedging research, airlines, utilities, fleets, assumes the hedger controls when and how much it consumes. Stored-value research forecasts how customers redeem prepaid balances, but stops at revenue recognition. A product that locks consumer prices on a volatile underlying sits exactly between the two: its hedge must be sized from a redemption forecast. No published model performs that coupling.
What the model does
A forecasting stage (seasonal ARIMA vs. LSTM) turns a two-year synthetic redemption panel into the two statistics a treasurer would actually hold: expected demand and forecast error. A Monte Carlo optimizer then chooses the hedge ratio minimizing a mean–dispersion objective over spot exposure, hedging premium, close-out of unused cover, margin capital, and redemption liquidity risk.
Headline findings
| Finding | Evidence |
|---|---|
| h* rises with price volatility | 0.80 → 0.90 down the high-uncertainty column as σ goes 0.10 → 0.45; monotone in every column |
| h* falls as demand gets harder to forecast | 1.00 → 0.80 across the medium-volatility row; hedging is abandoned entirely (h* = 0) when a poor forecast meets a quiet price |
| No static rule survives the grid | Not hedging forfeits up to 12.0% of the procurement budget at high volatility; full hedging bleeds up to 0.94% when demand is noisy |