Inflation Swaps

Inflation swaps come up when parties manage the risk of rising prices on inflation-linked liabilities or revenue. Pension funds and insurers with liabilities, and corporates with revenue, are the parties to these trades.

Exchanging the rate of inflation for a fixed rate

An inflation swap is a swap in which, for an agreed notional amount and term, one party pays an amount based on a fixed rate and the other pays an amount linked to the rate of increase in prices¹. The rise in prices is measured with a price index such as the consumer price index (CPI). The fixed rate is set in the market so that the trade is worth zero when it is agreed. As a result, no payments are exchanged when the trade starts¹. The general structure of swaps is covered in How Swaps Work.

Below, the party that pays the fixed-rate amount and receives the inflation-linked amount is called the inflation receiver¹. The party that pays the inflation-linked amount and receives the fixed-rate amount is called the inflation payer¹. Consider a hypothetical example in which Company C enters into the following inflation swap with Bank B. Company C is the inflation payer.

Zero-coupon swaps settle once at maturity

A zero-coupon swap is an inflation swap with a single payment at maturity. According to a 2013 paper from the Federal Reserve Bank of New York, it was the most commonly traded form in the US market². The inflation payer pays the notional amount multiplied by the rise in prices over the whole term. The inflation receiver pays the notional amount multiplied by the fixed rate compounded over the number of years in the term².

In the example, 1.02 raised to the 5th power is about 1.1041. Subtracting 1 and multiplying by 10 billion yen gives a fixed leg of about 1,040.81 million yen³. The inflation leg depends on the index in 5 years. If the index rises from 100 to 115, prices have risen 15%, and the amount is 1.5 billion yen. If the index rises only to 105, prices have risen 5%, and the amount is 500 million yen.

In practice, the two amounts are netted, and only the difference is paid by one party. The notional amount of 10 billion yen is not exchanged at the start or at maturity². If the index rises to 115, Company C pays Bank B about 459.19 million yen. If it rises to 105, Bank B pays Company C about 540.81 million yen.

Figure description

The payments of Company C, the inflation payer, on a zero-coupon inflation swap with a notional amount of 10 billion yen, a term of 5 years, and a fixed rate of 2% a year. Nothing is exchanged at the start of the trade. If the price index rises from 100 to 115 after 5 years, Company C receives the fixed leg of about 1,040.81 million yen from Bank B and pays the inflation leg of 1.5 billion yen to Bank B. In practice, Company C pays Bank B only the difference of about 459.19 million yen. The length of each arrow is a rough guide to the size of the amount. Bank B's payments run in the opposite direction to Company C's.

The two amounts are equal when prices rise at the same rate as the fixed rate, 2% a year compounded, on average over the term. For this reason, the fixed rate on a zero-coupon swap is used as a measure of what the market expects average inflation to be over the term⁴. However, besides the inflation outlook, the fixed rate also includes other elements, such as an extra amount for uncertainty about the future (a risk premium)⁵.

Deep diveThe formulas for zero-coupon swap payments

Let $N$ be the notional amount, $K$ the fixed rate, $T$ the number of years in the term, and $I_0$ and $I_T$ the price index at the start and at maturity. The two payments at maturity are as follows².

$$\text{Fixed leg} = N \times \{(1 + K)^T - 1\}$$ $$\text{Inflation leg} = N \times (I_T \div I_0 - 1)$$

Swaps that settle every year

Besides the form with a single payment at maturity, there is a form of inflation swap that settles every year during the term (some sources call it a multi-payment swap)⁶. As with a zero-coupon swap, one party pays an amount based on a fixed rate and the other pays an amount linked to prices.

Because these are OTC trades, the parties can shape the payments to their needs, and can also add a cap or a floor⁵. Even so, according to a 2006 Bank of England article, the standard trade for which the market quoted prices was the zero-coupon swap⁵.

The price index and the indexation lag

The price index that an inflation swap references is set for each currency. In most cases, it is a consumer price index that is not seasonally adjusted⁴.

The CPI-U, which US dollar trades reference, is the same index used by US inflation-linked bonds (TIPS)¹. In the euro area, besides the euro area HICP excluding tobacco, the French CPI excluding tobacco is also used, as with French government inflation-linked bonds⁷. Japanese trades reference a consumer price index that includes the effect of consumption tax increases⁸.

A price index is published only after the month has ended. Japan's nationwide consumer price index for a month is, as a rule, published on the Friday of the week that includes the 19th of the following month⁹. In the United States, too, the CPI for a month is not known until the middle of the following month¹⁰. For this reason, inflation swaps do not use prices on the start date or the maturity date, but the index for an earlier month. In US trades, payments are based on inflation from three months before the start date to three months before the maturity date¹¹. This delay is called the indexation lag. How inflation-linked bonds work is covered in Inflation-Indexed JGBs and BEI.

What changes the value

The profit or loss on an inflation swap depends on whether actual inflation turns out higher or lower than the fixed rate. If average inflation over the term is above the fixed rate, the inflation receiver receives the difference. If it is below, the inflation payer does. In the example, Bank B received the difference when the index rose to 115, and Company C received it when the index rose to 105.

Before maturity, a change in the inflation outlook changes the fixed rate on new trades agreed at that time⁴. When the outlook rises, the fixed rate on new trades rises, so trades agreed earlier gain value for the inflation receiver and lose value for the inflation payer. When the outlook falls, the reverse happens.

What inflation swaps are used for

Inflation swaps are used to transfer inflation risk. Pension funds and insurers that must make inflation-linked payments receive the inflation leg, to cover the higher cost they face when prices rise. Firms with inflation-linked assets or revenue, such as utilities, pay the inflation leg, to cover the shortfall in revenue if prices do not rise¹²¹³. In the United Kingdom, pension payments are often linked to rises in retail prices, and pension funds accounted for much of the demand for inflation swaps (according to a 2006 source)¹⁴. Some parties take on inflation risk for speculation, betting on how prices will move, or to diversify their investments¹².

In Company C's example, suppose that 10 billion yen of Company C's revenue grows in line with the price index over 5 years. If the index rises to 115, revenue increases by 1.5 billion yen, but Company C pays a net of about 459.19 million yen on the swap, so the combined increase is about 1,040.81 million yen. If the index rises only to 105, revenue increases by only 500 million yen, but Company C receives about 540.81 million yen on the swap, so the combined increase is again about 1,040.81 million yen. Whichever way prices move, the swap fixes Company C's revenue increase at the amount that 2% a year compounded would give. In return, when prices rise sharply, the swap payment cancels out the extra revenue.

Inflation risk can also be transferred with inflation-linked bonds. Inflation swaps let the parties set terms such as the maturity and notional amount for each trade, so they can be closely matched to the user's needs¹². Also, buying or selling an inflation-linked bond involves exchanging the full principal, while an inflation swap settles only the difference at maturity¹⁵.

Counterparty risk and market practice

Inflation swaps are OTC derivatives, traded without going through an exchange. In the US market, large dealers quote prices to customers, and dealers often trade with one another through brokers¹⁶.

In Japan, data on inflation swap rates for terms of 1 to 10 years are available continuously from March 2007. However, the Japanese inflation swap market is less active than even the market for inflation-indexed JGBs¹⁷.

Because these are OTC trades, each party bears the risk that the other party fails to pay as agreed (counterparty credit risk). A zero-coupon swap has no payments until maturity, so a large move in prices can build up a large difference to be received at maturity. This risk is usually reduced by exchanging collateral¹⁸.

Notes

1. Fleming and Sporn, "Trading Activity and Price Transparency in the Inflation Swap Market" (Federal Reserve Bank of New York, Economic Policy Review, May 2013), page 47, "2. Inflation Swaps." ↩ ↩² ↩³ ↩⁴ ↩⁵

2. Fleming and Sporn (May 2013), page 47, "2. Inflation Swaps," and the chart "Zero-Coupon Inflation Swap Cash Flows (at Maturity)." ↩ ↩² ↩³ ↩⁴

3. 1.02 raised to the 5th power is 1.10408..., so the fixed leg is 1,040,808,032 yen. The text and tables round it to the nearest 10,000 yen. ↩

4. Böninghausen et al., "Interpreting recent developments in market based indicators of longer term inflation expectations" (European Central Bank, Economic Bulletin, Issue 6/2018), Section 2. ↩ ↩² ↩³

5. Hurd and Relleen, "New information from inflation swaps and index-linked bonds" (Bank of England, Quarterly Bulletin Spring 2006), page 26, "Using market rates on inflation swaps." ↩ ↩² ↩³

6. European Central Bank, "Deriving euro area inflation expectations from inflation-linked swaps" (Monthly Bulletin, September 2003, Box 4), page 31. The source calls the form that pays every year a multi-payment I/L swap. ↩

7. European Central Bank (September 2003), page 31. This describes the situation as of September 2003. ↩

8. Kazuhiro Hiraki and Wataru Hirata, "ブレークイーブン・インフレ率から抽出される日本の市場参加者の長期インフレ予想" (Long-term inflation expectations of market participants in Japan extracted from breakeven inflation rates) (Bank of Japan Working Paper Series No.20-J-6, September 2020, in Japanese), note 8 on page 7. ↩

9. Statistics Bureau of Japan, "消費者物価指数に関するQ&A（回答）" (Q&A on the consumer price index, in Japanese), C-1. ↩

10. Diercks et al., "The Swaps Strike Back: Evaluating Expectations of One-Year Inflation" (Board of Governors of the Federal Reserve System, Finance and Economics Discussion Series 2023-061), page 8. ↩

11. Fleming and Sporn (May 2013), note 7 on page 47. ↩

12. Fleming and Sporn (May 2013), page 47. ↩ ↩² ↩³

13. European Central Bank (September 2003), page 31. This describes the euro area market in 2002. ↩

14. Hurd and Relleen (Spring 2006), page 25, and the box "Pension fund valuation and liability driven investment strategies" on pages 8–9 of the same issue. ↩

15. Diercks et al. (2023-061), page 7. ↩

16. Fleming and Sporn (May 2013), page 47. This describes the US market as of May 2013. ↩

17. Hiraki and Hirata (September 2020), pages 7–8. This describes the situation as of September 2020. ↩

18. European Central Bank (September 2003), page 31. This describes the situation as of September 2003. ↩