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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.

Suggested Citation

  • Zvi Bodie, 1989. "Inflation Insurance," NBER Working Papers 3009, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:3009
    Note: ME
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    References listed on IDEAS

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    1. Zvi Bodie, 1982. "Investment Strategy in an Inflationary Environment," NBER Chapters, in: The Changing Roles of Debt and Equity in Financing U.S. Capital Formation, pages 47-64, National Bureau of Economic Research, Inc.
    2. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    3. Martin Feldstein, 1983. "Should Private Pensions Be Indexed?," NBER Chapters, in: Financial Aspects of the United States Pension System, pages 211-230, National Bureau of Economic Research, Inc.
    4. Hemming, Richard & Kay, John A, 1982. "The Costs of the State Earnings Related Pension Scheme," Economic Journal, Royal Economic Society, vol. 92(366), pages 300-319, June.
    5. Feldstein, Martin & Liebman, Jeffrey B., 2002. "Social security," Handbook of Public Economics, in: A. J. Auerbach & M. Feldstein (ed.), Handbook of Public Economics, edition 1, volume 4, chapter 32, pages 2245-2324, Elsevier.
    6. Zvi Bodie, 1988. "Inflation, Index-Linked Bonds, and Asset Allocation," NBER Working Papers 2793, National Bureau of Economic Research, Inc.
    7. Joseph B. Grolnic & Alicia H. Munnell, 1986. "Should the U.S. government issue index bonds?," New England Economic Review, Federal Reserve Bank of Boston, issue Sep, pages 3-21.
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    Cited by:

    1. Jeffrey R. Brown & Olivia S. Mitchell & James M. Poterba, 2001. "The Role of Real Annuities and Indexed Bonds in an Individual Accounts Retirement Program," NBER Chapters, in: Risk Aspects of Investment-Based Social Security Reform, pages 321-370, National Bureau of Economic Research, Inc.
    2. Barr, Nicholas, 1992. "Economic theory and the welfare state : a survey and interpretation," LSE Research Online Documents on Economics 279, London School of Economics and Political Science, LSE Library.
    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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