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Chapter 2 The CPI Linkage, the Concept of Break-even Inflation and the Deflation Floor

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Inflation-Linked Bonds and Derivatives
This chapter is in the book Inflation-Linked Bonds and Derivatives
Chapter 2The CPI Linkage, the Concept of Break-evenInflation and the Deflation FloorAs discussed in the first chapter, all cash-flows of index-linked products are tied to aconsumer price index, which captures the changes in the prices of goods and serv-ices. In this chapter we go into the detail of how to calculate these reference indicesand how index-linked bonds ensure investors receive a certain real return. We thengo on to discuss break-even inflation, which links traded inflation products to thereal world, and following on from this, the deflation floor, which comprises theunique behavior of products whose strike levels lie close to or at the zero value ofactual inflationthe border between inflationary and deflationary environments.The CPI LinkageConsumer price indices (CPI or HICPx) are only published with a time lag as thestatisticians require time to gather the relevant data and compute the indices. The(unrevised) CPIs (ex tobacco) are therefore applied with a three-month time lag tocompute cash-flows in the euro area and most other linker markets.An example: The Apr-21 HICPx index is used for July 21. To be precise, thisindex is used for calculating the reference index for the first day of the month, inthis example 1 July. Similarly, the May-21 HICPx index will be used as the referenceindex for August 1. For every trading day in between those dates, a daily referenceindex is calculated by linear interpolation. This is done via the following formula:RefCPIt,m=CPIm3+d1Dm×CPIm2CPIm3ðÞwhereCPImdenotes the respective lagged price index level,Dmthe number of daysin the settlement month anddthe respective day of the settlement month.For example, the Apr-21 HICPx (used for July 1) is 106.69, the May-21 index (ap-plied to August 1) 106.97. The reference index for July 12, 2021 is therefore 106.78935(note that the convention is to calculate the index to the 5th decimal). The referenceindex for the first settlement day of an index-linked bond is called the base index.The question of how much inflation has taken place since a bond was launchedis measured by the progression of the reference index relative to the bondsbaseindex level. In order to capture the inflation accrual between two points in time, thehttps://doi.org/10.1515/9783110787429-002
© 2023 Walter de Gruyter GmbH, Berlin/Boston

Chapter 2The CPI Linkage, the Concept of Break-evenInflation and the Deflation FloorAs discussed in the first chapter, all cash-flows of index-linked products are tied to aconsumer price index, which captures the changes in the prices of goods and serv-ices. In this chapter we go into the detail of how to calculate these reference indicesand how index-linked bonds ensure investors receive a certain real return. We thengo on to discuss break-even inflation, which links traded inflation products to thereal world, and following on from this, the deflation floor, which comprises theunique behavior of products whose strike levels lie close to or at the zero value ofactual inflationthe border between inflationary and deflationary environments.The CPI LinkageConsumer price indices (CPI or HICPx) are only published with a time lag as thestatisticians require time to gather the relevant data and compute the indices. The(unrevised) CPIs (ex tobacco) are therefore applied with a three-month time lag tocompute cash-flows in the euro area and most other linker markets.An example: The Apr-21 HICPx index is used for July 21. To be precise, thisindex is used for calculating the reference index for the first day of the month, inthis example 1 July. Similarly, the May-21 HICPx index will be used as the referenceindex for August 1. For every trading day in between those dates, a daily referenceindex is calculated by linear interpolation. This is done via the following formula:RefCPIt,m=CPIm3+d1Dm×CPIm2CPIm3ðÞwhereCPImdenotes the respective lagged price index level,Dmthe number of daysin the settlement month anddthe respective day of the settlement month.For example, the Apr-21 HICPx (used for July 1) is 106.69, the May-21 index (ap-plied to August 1) 106.97. The reference index for July 12, 2021 is therefore 106.78935(note that the convention is to calculate the index to the 5th decimal). The referenceindex for the first settlement day of an index-linked bond is called the base index.The question of how much inflation has taken place since a bond was launchedis measured by the progression of the reference index relative to the bondsbaseindex level. In order to capture the inflation accrual between two points in time, thehttps://doi.org/10.1515/9783110787429-002
© 2023 Walter de Gruyter GmbH, Berlin/Boston
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