Working Paper: NBER ID: w3009
Authors: 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. \nWhen 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. \nThe 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.
Keywords: inflation insurance; forward contract; call option; put option; contingent claim; deductible; cap; futures contract; CPI; dynamic hedging; portfolio rebalancing
JEL Codes: G13; E31
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| Inflation insurance contract (E31) | European call option on CPI (G13) |
| Price of inflation insurance policy (E31) | Time to maturity (C41) |
| Price of inflation insurance policy (E31) | Real interest rate (E43) |
| Price of inflation insurance policy (E31) | Expected rate of inflation (E31) |
| Price of inflation insurance policy (E31) | Real risk premium on nominal bonds (E43) |
| Insurance policy with deductible (G52) | Cannot be priced as simple forward contract on CPI (G13) |
| Option feature value (Y60) | Deductible near forward rate of inflation (G52) |
| Approach (Y20) | Quantification of costs associated with indexing pension benefits for inflation (J32) |
| Approach (Y20) | Estimating savings for social security system from introducing deductibles (H55) |