Overview of Commodity Derivatives

Commodity derivatives are used by trading companies that sell futures to protect against a fall in the price of imported soybeans, manufacturers that guard against rising raw material prices, and investors that add commodities to a portfolio as protection against inflation.

Classification of commodities

Commodities are physical assets such as energy resources, metals, and grains. A commodity derivative is a derivative whose underlying asset is a commodity or its price. Unlike stocks and bonds, commodities are physical goods that get consumed, so their prices reflect consumer demand, supply constraints, storage costs, and seasonal patterns in supply and demand¹. The main commodities traded on exchanges fall into the following three groups².

In this classification, electricity and emission allowances belong to energy. Electricity is hard to store, so the spot price can jump when demand exceeds the limit of supply. Natural gas and kerosene have strong seasonality: their futures prices rise for the periods when demand is high¹. Benchmarks and markets for crude oil and natural gas are covered in Energy: Crude Oil and Natural Gas.

Exchange trading and OTC trading

Commodity derivatives include futures and options traded on exchanges, and forward contracts, swaps, and options that the parties enter into directly without an exchange²³⁴. For exchange trades, each product has detailed rules for the quantity per trade and the location and method of delivery, so that quality and settlement are standardized. Over-the-counter trades are bilateral contracts, so the parties can set the terms freely, and many forms exist to meet the different needs of producers and users. According to a 2010 paper by the Institute for Monetary and Economic Studies of the Bank of Japan, producers and users sometimes contract with each other directly, but the counterparty is often an intermediary such as a trading company, a financial institution, or a broker².

Futures and forwards are both contracts to exchange a set quantity for a set amount of money at a set future date³. For futures, the exchange acts as the clearing house and handles clearing, mark-to-market, and margin, while in a bilateral forward each party bears the credit risk of its counterparty³.

In an over-the-counter swap on a commodity (a commodity swap), one party receives an amount calculated from the then-current spot price of a set quantity of the commodity and pays a fixed amount⁵. Other trades include spread trades on the price difference between a raw material and its product, and options that reference the average price over a set period (Asian options). Asian options are used because users care about the average price over the period in which they use the commodity⁶.

Settlement methods at expiry

If you hold exchange-traded commodity futures until the last trading day, the contract settles, depending on the product, either by physical delivery of the commodity or by cash settlement, in which the price difference is paid or received in cash. Take the gold futures on Osaka Exchange as an example. Gold Standard Futures settle by physical delivery (the exchange's rules classify them as physical futures), and Gold Mini Futures settle in cash (classified as contract-month cash-settled futures, settled by paying and receiving money at expiry)⁷.

The trading unit of Gold Standard Futures is 1kg, and the gold delivered is gold bullion in 1,000g bars with a purity of 99.99% or higher⁸. Consider a hypothetical example in which Company D buys one Gold Standard Futures contract and does not sell it before the last trading day. On the delivery date, both the seller and Company D settle with Japan Securities Clearing Corporation (JSCC), the central counterparty. The seller submits to JSCC a warehouse receipt issued by a warehouse the exchange has designated. Company D pays JSCC the delivery payment calculated from the delivery price⁸⁹.

Figure description

This shows how the seller (the deliverer) and the buyer, Company D (the receiver), who both held Gold Standard Futures until the last trading day, settle with the central counterparty JSCC on the delivery date. The seller submits to JSCC a warehouse receipt for gold bullion issued by a designated warehouse ("Gold receipt" in the figure) and receives the delivery payment from JSCC. Company D pays the delivery payment to JSCC and receives the warehouse receipt. The seller and Company D do not deal with each other directly. They exchange the title to the physical gold and the payment through the central counterparty.

If Company D instead buys one Gold Mini Futures contract (trading unit 100g) and holds it, no physical gold changes hands. Gold Mini Futures are futures on the price of Gold Standard Futures for the same contract month. On the day after the last trading day, the opening price of that day's Gold Standard Futures trading (the day session) becomes the price used for settlement (the final settlement price), and the parties pay or receive an amount based on the difference from the purchase price⁷¹⁰. Consider a hypothetical example in which Company D buys at 10,000 yen per gram. If the final settlement price is 11,000 yen per gram, the difference of 1,000 yen times 100g gives a gain of 100,000 yen. If the final settlement price is 9,000 yen per gram, Company D loses the same 100,000 yen.

You can also close out a futures position before the last trading day with an opposite trade. By selling what you bought, or buying back what you sold, you pay or receive the difference between the original price and the price of the offsetting trade and leave the position. In Japanese, this payment of the difference is also called sakin kessai (settlement by difference)¹¹. The Japanese term sakin kessai is used for settlement at expiry as well as for the difference on an offsetting trade. Osaka Exchange also uses it for the final settlement of Nikkei 225 VI Futures, futures on the Nikkei Stock Average Volatility Index (Nikkei 225 VI)¹².

Futures prices and the convenience yield

The price of commodity futures is set at the spot price plus the funding cost and the storage cost of holding the physical commodity until maturity, minus the benefit of having the physical commodity on hand¹³. Consider a hypothetical example in which a commodity's spot price is 100,000 yen per ton, you can borrow for one year at 2% a year, and storing one ton in a warehouse for one year costs 3,000 yen. The funding cost is 100,000 yen × 2%, or 2,000 yen. Leaving aside the benefit of holding the commodity, the futures price for delivery in one year is 100,000 + 2,000 + 3,000, or 105,000 yen.

For futures on financial assets, the futures price is often derived from the funding cost and income such as interest, as explained in Forwards and Futures. For commodities, the storage cost and the value of having a usable physical commodity on hand come on top of these¹³.

The value of having the physical commodity on hand, expressed as a yield, is called the convenience yield. The value of holding the physical commodity, and so the convenience yield, is higher for goods that are hard to store, goods whose inventories have run low, and goods that are hard to obtain quickly when needed¹³. In the earlier example, if the benefit of holding the physical commodity for one year is worth 8,000 yen per ton (a convenience yield of 8% a year), the futures price is 105,000 − 8,000, or 97,000 yen, which is lower than the spot price.

Deep diveThe futures price with continuous compounding

Let $S$ be the spot price, $T$ the number of years to maturity, $r$ the risk-free rate, $c$ the storage cost expressed as a yield, and $\varepsilon$ the convenience yield. The futures price $F$ can then be written as follows¹⁴.

$$F = S e^{(r + c - \varepsilon)T}$$

The example in the main text approximates this relationship with annual simple interest and expresses the storage cost and the convenience yield as amounts of money. Because the storage cost is hard to observe directly, the convenience yield minus the storage cost is sometimes combined into $\delta = \varepsilon - c$. In that case, $\delta$ can be backed out from the spot and futures prices and interest rates observed in the market¹⁴.

Contango and backwardation

When futures prices are higher for more distant (deferred) contract months, the shape is called contango, and when they are lower for more distant months, it is called backwardation. If you treat the spot price as the nearest delivery, then in the example in the previous section, a futures price of 105,000 yen, above the spot price of 100,000 yen, corresponds to contango, and a futures price of 97,000 yen, below the spot price, corresponds to backwardation. Backwardation appears when the convenience yield is larger than the sum of the funding cost and the storage cost¹⁵.

Backwardation tends to appear when supply and demand are tight (the spot price is high and inventories are low), and contango tends to appear when supply and demand loosen. When supply and demand are tight, holding the physical commodity is worth more even after paying the storage cost, so the convenience yield is higher. According to the 2010 paper by the Institute for Monetary and Economic Studies, observed commodity futures prices are often lower for more distant months, which indicates that the convenience yield tends to be higher than interest rates¹⁵.

The shape changes over time, even for the same commodity. WTI crude oil futures prices were in contango on January 4, 1999, and in backwardation on January 2, 2008¹⁶. Futures prices can also form shapes that neither simply rise nor simply fall, such as prices that rise up to a certain deferred month and fall after that¹⁶.

Users: producers, consumers, and investors

The main users of commodity derivatives are those who produce and sell commodities, those who buy them as raw materials, and investors who hold them as investments. Producers and distributors use futures to hedge against falling prices, and manufacturers to hedge against rising raw material prices¹⁷¹.

In a selling hedge, you sell futures in advance and buy them back when you sell the physical commodity. For example, a trading company that imports and sells US soybeans sells futures in advance to protect against a price fall during shipping¹⁷. If the spot price falls, the gain on the futures makes up for the lower sales proceeds from the physical soybeans¹⁸. If the spot price rises instead, the loss on the futures cancels out the higher sales proceeds, so the company receives less than it would have without the hedge.

Investors hold commodities as investments to protect against inflation risk and because commodity prices tend to move only loosely with stocks and bonds¹. There are also commodity indices built from the prices of representative futures, and bonds whose payments are linked to a commodity index (commodity-linked bonds)¹⁹. An investor who buys futures gains if the price rises and loses if it falls.

Commodity futures trading can produce large gains or losses even when prices move only a little²⁰.

Notes

1. Institute for Monetary and Economic Studies, Bank of Japan, "コモディティ価格変動の特徴とプライシング・モデルの展開" (Features of commodity price movements and developments in pricing models), Kinyu Kenkyu (April 2010), "1. はじめに" (Introduction), page 28 (in Japanese). ↩ ↩² ↩³ ↩⁴

2. Institute for Monetary and Economic Studies, Bank of Japan, "コモディティ価格変動の特徴とプライシング・モデルの展開," "2.（1）コモディティ市場の概観" (Overview of commodity markets) and Table 1, "商品取引所におけるコモディティ取引の事例" (Examples of commodity trading on commodity exchanges), page 29 (in Japanese). ↩ ↩² ↩³

3. Institute for Monetary and Economic Studies, Bank of Japan, "コモディティ価格変動の特徴とプライシング・モデルの展開," "2.（2）さまざまなコモディティ取引" (Various commodity trades), page 31 (in Japanese). ↩ ↩² ↩³

4. "商品先物取引法" (Commodity Derivatives Transaction Act, in Japanese), Article 2, paragraph 14. The Act defines "店頭商品デリバティブ取引" (over-the-counter commodity derivatives transactions) as transactions conducted outside a commodity market and similar markets, including sales in which a commodity and payment for it are delivered at a future time (item 1), options (item 4), and transactions in which the parties pay each other money based on the rate of change in a commodity's price (item 6). An English translation is available: "Commodity Derivatives Transaction Act" (Japanese Law Translation, https://www.japaneselawtranslation.go.jp/en/laws/view/3191/je); it reflects amendments only up to Act No. 86 of 2012. ↩

5. Martin Haugh, "Forwards, Swaps, Futures and Options" (lecture notes for IEOR E4706, Columbia University, 2016), page 5, Example 3. ↩

6. Institute for Monetary and Economic Studies, Bank of Japan, "コモディティ価格変動の特徴とプライシング・モデルの展開," "2.（2）さまざまなコモディティ取引" (Various commodity trades), pages 31–32 (in Japanese). ↩

7. Osaka Exchange, "商品先物取引制度要綱" (Outline of the commodity futures trading system, in Japanese; as of April 13, 2026), "Ⅰ 1 (1) 取引の種類等" (Types of trading), page 1, and "(2) 標準品等" (Standard grades), "②限月現金決済先物取引における取引の対象" (Underlying of cash-settled futures), pages 2–3. ↩ ↩²

8. Osaka Exchange, "商品先物取引制度要綱" (in Japanese), "6 (1) 取引単位" (Trading unit), page 5, and "8 (1) 現物先物取引における受渡決済" (Delivery settlement in physical futures), "① 受渡決済" (Delivery settlement) and "② 受渡供用品" (Deliverable goods), page 9. ↩ ↩²

9. Osaka Exchange, "制度概要" (Outline, in Japanese) for Gold Standard Futures (updated April 13, 2026), "受渡場所" (Delivery location) and "受渡方法" (Delivery method). ↩

10. Osaka Exchange, "商品先物取引制度要綱" (in Japanese), "8 (2) 限月現金決済先物取引の取引における最終決済" (Final settlement of cash-settled futures), page 11, and "6 (1) 取引単位" (Trading unit), page 5. ↩

11. Ministry of Agriculture, Forestry and Fisheries, "商品先物取引とは" (What are commodity futures?, in Japanese), "先物取引の仕組み" (How futures trading works), and "用語解説" (Glossary), "反対売買" (Offsetting trade) and "差金決済" (Settlement by difference). ↩

12. Osaka Exchange, "日経平均ボラティリティー・インデックス先物取引の利用のコツ" (Tips for using Nikkei Stock Average Volatility Index futures, in Japanese; 4th edition, November 2024), "日経平均VI先物取引制度概要" (Outline of Nikkei 225 VI Futures), "最終決済" (Final settlement), page 14. ↩

13. Institute for Monetary and Economic Studies, Bank of Japan, "コモディティ価格変動の特徴とプライシング・モデルの展開," "2.（3）イ. 先物価格の期間構造" (Term structure of futures prices), pages 33–34 (in Japanese). ↩ ↩² ↩³

14. Institute for Monetary and Economic Studies, Bank of Japan, "コモディティ価格変動の特徴とプライシング・モデルの展開," equation (1) in "2.（3）イ." and the text around it, page 34 (in Japanese). The paper's $F(t, T)$, $S(t)$, and $T - t$ are written here as $F$, $S$, and $T$. ↩ ↩²

15. Institute for Monetary and Economic Studies, Bank of Japan, "コモディティ価格変動の特徴とプライシング・モデルの展開," "2.（3）イ. 先物価格の期間構造" (Term structure of futures prices), page 34 (in Japanese). ↩ ↩²

16. Institute for Monetary and Economic Studies, Bank of Japan, "コモディティ価格変動の特徴とプライシング・モデルの展開," Figure 3, "WTI 原油の先物カーブ" (WTI crude oil futures curves), page 35, and the explanation around Figure 5, page 36 (in Japanese). ↩ ↩²

17. Ministry of Agriculture, Forestry and Fisheries, "商品先物取引とは" (What are commodity futures?, in Japanese), "Q＆A", Q4. ↩ ↩²

18. Ministry of Agriculture, Forestry and Fisheries, "商品先物取引とは" (What are commodity futures?, in Japanese), "先物市場の役割" (The role of futures markets), "(イ)価格変動リスクの抑制（ヘッジ）機能" (The function of limiting price risk: hedging). ↩

19. Institute for Monetary and Economic Studies, Bank of Japan, "コモディティ価格変動の特徴とプライシング・モデルの展開," "2.（2）さまざまなコモディティ取引" (Various commodity trades), page 33 (in Japanese). ↩

20. Ministry of Agriculture, Forestry and Fisheries, "商品先物取引とは" (What are commodity futures?, in Japanese), "Q＆A", Q5. ↩