Why Calendar Spreads Are Not Always Arbitrage in Commodities

Summary

The document asks whether calendar spreads become pure arbitrage when implied volatility is flat across strikes and maturities, as in the Black–Scholes framework. Its answer cautions that equal implied volatility across maturities does not guarantee that contracts for different delivery periods are economically interchangeable. In commodities, differences between delivery-month prices can reflect storage costs and convenience yield. A trader might buy a commodity for near-term delivery, store it, and sell it for a later delivery month; the economics of this trade depend on whether the price difference covers storage and other costs.

Electricity provides a stronger limitation: it is difficult to store electricity from one delivery period for use in another. Contracts for separate months therefore need not converge in the way closely linked assets might. The discussion is conceptual and gives no pricing model, data, or conditions for establishing arbitrage. Its examples show why volatility assumptions alone cannot determine whether a calendar spread is risk-free; delivery mechanics and carry economics matter.

Key ideas

• Equal implied volatility across maturities does not by itself establish calendar-spread arbitrage.
• Storage costs and convenience yield can explain differences between commodity delivery months.
• A storage trade can lock in a spread only when the delivery prices cover the relevant costs.
• Electricity is difficult to store across delivery periods, weakening links between monthly contracts.

Tags

# Calendar spreads under black scholes world


# Calendar spreads under black scholes world












If IV skew is flat (all strikes with the same IV ss ATM) as in the black-scholes world for all maturities, would calendar spreads be considered as pure arbitrage?

## Answer by Rylan (score 1)

https://quant.stackexchange.com/a/76562

In commodities, it's not necessarily arbitrage.

In the example of oil, if oil has a very low price for delivery in March and a very high price for delivery in April, you may in fact be able to lock in a profit by taking delivery of the oil in March, paying to store it until April, and then selling it in April. This is often formalized using the convenience yield.

An even more extreme example is electricity futures, where it's more difficult to store electricity delivered in one month for consumption in another month. Without diving into the modelling details, intuitively you can think of contracts that deliver in two different months as being fundamentally not that closely linked, and in particular, there isn't any reason why convergence should occur even if both have the same implied vol.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.