Hedging size risk: Theory and application to the US gas market

- Exposure to combined price and size risk sources is considered.
- An optimal custom hedge is derived as a claim on price and a size-linked index.
- Optimal price-based forward and price-index forward hedges are computed.
- Analytical expressions and comparative statics are developed in a market model.
- A performance analysis of the optimal hedge is conducted in the US gas market.

Many corporate commitments exhibit a combined financial exposure to both market prices and idiosyncratic size components (e.g., volume, load, or business turnover). We design a customized contract to optimally mitigate the risk of joint fluctuations in price and size terms. The hedge is sought out among contingent claims written on price and any quoted index that is statistically dependent on commitment size. Closed-form solutions are derived for the optimal custom hedge pay-off and for the asset holdings of two market strategies, one based on price-linked forwards, the other based on price-linked and index-linked forwards. Analytical hedges are obtained using a stylized lognormal market model. Detailed comparative statics provide a thorough analysis of optimal hedging pay-off functions. Performance assessment is conducted in the context of the US gas market and a prototypical urban region. Results suggest that hedging through suitable custom claims written on price and an additional index significantly outperforms standard price-based as well as mixed price-index forward hedging alternatives. Our optimal custom hedge could be adopted as a benchmark for the relative assessment of any risk management solution.