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Inflation Insurance

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  • Zvi Bodie

Abstract

A contract to insure $1 against inflation is equivalent to a European call option on the consumer price index. When there is no deductible this call option is equivalent to a forward contract on the CPI. Its price is the difference between the prices of a zero coupon real bond and a zero coupon nominal bond, both free of default risk. Provided that the risk-free real rate of interest is positive, the price of such an inflation insurance policy first rises and then falls with time to maturity. It is a decreasing function of the real interest rate and an increasing function of both the expected rate of inflation and the real risk premium on nominal bonds. When a deductible is introduced, the insurance policy can no longer be priced like a CPI forward contract. The option feature has its greatest value when the deductible is close to the forward rate of inflation, defined as the difference between the risk-free nominal and real interest rates. Such inflation insurance contracts are priced using the model developed by Black-Merton-Scholes. Pricing an inflation insurance policy with a cap requires only a minor modification of the model. The approach presented in this paper permits fairly precise quantification of the cost of implementing proposals to index pension benefits for inflation. It also gives us a way of estimating the savings to the Social Security system that would result from introducing a deductible.

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Bibliographic Info

Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 3009.

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Date of creation: Jun 1989
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Publication status: published as The Journal of Risk and Insurance, December 1990.
Handle: RePEc:nbr:nberwo:3009

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  1. Alicia H. Munnell & Joseph B. Grolnic, 1986. "Should the U.S. government issue index bonds?," New England Economic Review, Federal Reserve Bank of Boston, Federal Reserve Bank of Boston, issue Sep, pages 3-21.
  2. Zvi Bodie, 1982. "Investment Strategy in an Inflationary Environment," NBER Working Papers 0701, National Bureau of Economic Research, Inc.
  3. Feldstein, Martin & Liebman, Jeffrey B., 2002. "Social security," Handbook of Public Economics, Elsevier, in: A. J. Auerbach & M. Feldstein (ed.), Handbook of Public Economics, edition 1, volume 4, chapter 32, pages 2245-2324 Elsevier.
  4. Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, The RAND Corporation, vol. 4(1), pages 141-183, Spring.
  5. Martin Feldstein, 1981. "Should Private Pensions Be Indexed?," NBER Working Papers 0787, National Bureau of Economic Research, Inc.
  6. Zvi Bodie, 1988. "Inflation, Index-Linked Bonds, and Asset Allocation," NBER Working Papers 2793, National Bureau of Economic Research, Inc.
  7. Hemming, Richard & Kay, John A, 1982. "The Costs of the State Earnings Related Pension Scheme," Economic Journal, Royal Economic Society, Royal Economic Society, vol. 92(366), pages 300-319, June.
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Cited by:
  1. Nicholas Barr, 1992. "Economic theory and the welfare state : a survey and interpretation," LSE Research Online Documents on Economics, London School of Economics and Political Science, LSE Library 279, London School of Economics and Political Science, LSE Library.
  2. Jeffrey R. Brown & Olivia S. Mitchell & James M. Poterba, 1999. "The Role of Real Annuities and Indexed Bonds in an Individual Accounts Retirement Program," Center for Financial Institutions Working Papers, Wharton School Center for Financial Institutions, University of Pennsylvania 99-18, Wharton School Center for Financial Institutions, University of Pennsylvania.
  3. Jeffrey R. Brown & Olivia S. Mitchell & James M. Poterba, 2000. "Mortality Risk, Inflation Risk, and Annuity Products," NBER Working Papers 7812, National Bureau of Economic Research, Inc.
  4. Robert J. Shiller, 1997. "Public Resistance to Indexation: A Puzzle," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 28(1), pages 159-228.

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