Face Value Guarantee for the Inflation-Indexed Government Bonds

Real Options on Consumer Price Index

Abstract

In this paper, we first overview several issues related to price-linked government bonds in several countries in terms of the policy background and conditions of issuance, then we discuss risk premium and principal guarantee option when extracting the expected inflation rate by Break-Even Inflation rate (BEI) . When we try to derive the pricing model for the principal guarantee option premium, we employ the pricing kernel (SDG: Stochastic Discount Factor) approach. Therefor we can obtain the value of guarantee as a put option pricing formula by maximizing the expected utility from consumption of representative investors. Regardless of the fact that we assumed the investors are risk averse, it is possible to derive risk neutral valuation formula, which is free from the risk preference and the expectation of the investors. We also derive the exact formula for the future deflation probability embedded in the equilibrium price. It can be shown that necessary information to compute the probability comes from the market price of actual nominal discount bonds and inflation-indexed government bonds only. We also discussed the possibility of estimating the degree of risk aversion of the representative investors based on the Japanese government bond price.