Contingent claims valuation when the payoff depends on the price level: An index-linked bond approach

This paper analyses how to price contingent claims, the payoffs which depend on the price level, by using an index-linked bond as the underlying asset. The analysis takes place in an economy where the nominal instantaneous rate of interest (the spot rate) is stochastic. A closed formula for options is presented as well as an investigation of how sensitive this formula is to variations in the parameters of the formula. It turns out that the volatility of the index-linked bond price heavily affects the option price and that the correlation between the spot rate and the return of the index-linked bond is of potential importance. Different areas of application, such as loan contracts in the housing sector and inflation insurances in pension plans, are also discussed.