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.
Key words: Inflation, insurance, forward contract, call
option, put option, contingent claim, deductible,
cap, futures contract, CPI, dynamic hedging,
In order to set up a list of libraries that you have access to,
you must first login
or sign up.
Then set up a personal list of libraries from your profile page by
clicking on your user name at the top right of any screen.