Do Volatility Smiles Matter for Pricing Asian Basket Options? The Case of Livestock Gross Margin Insurance for Dairy Cattle

Livestock Gross Margin Insurance for Dairy Cattle (LGM-Dairy) is Asian basket option-like insurance tool that enables U.S. dairy producers to protect income-over-feed-costs margins. While LGM-Dairy rating method assumes flat implied volatility curves for all marginal price distributions, substantial evidence suggests upward-bending skews in implied volatility curves are typical and expected features of options written on futures for storable commodities. In this article we examine if accounting for volatility skews and smiles substantially influence actuarially fair premiums for LGM-Dairy insurance. Presence of strong asymmetry or excess kurtosis indicates higher likelihood of extreme events. Consequently, actuarially fair premiums for insurance products designed to protect only against catastrophic losses may be higher. As most users of LGM-Dairy treat this product as catastrophic margin risk insurance, it is important to understand the impact of distributional assumptions on LGM-Dairy premiums. We calculate LGM-Dairy premiums under flexible milk and feed marginal distributions, while maintaining all other elements of the official LGM-Dairy rating method. We find LGM-Dairy premiums to be very robust to assumptions regarding volatility skews. Our simulations reveal that basket option nature of LGM-Dairy suffices to neutralize the effects of volatility skews on LGM-Dairy premiums. Therefore, while lognormality assumption is inconsistent with observed option prices, it remains a useful heuristic that does not bias LGM-Dairy premiums in a financially important way.