This paper presents a tractable model in closed form for pricing inflation indexed bonds, swaps and options. In keeping with empirical evidence, the model predicts that deflation is unlikely. Various model variants have been presented in this paper. Inflation may `jump'. Nominal interest rates may be modeled through a Gaussian model, a quadratic model, etc. Closed-form solutions for inflation indexed bonds, swaps and options have been presented in both continuous and discrete time settings. In discrete time, the model can be estimated more easily, the market price of inflation risk can be specified with more freedom, and as in continuous time, a change of measure provides the closed-form solutions for European type inflation options and options on nominal bonds.

Global markets for inflation indexed bonds and inflation indexed derivatives have considerably developed in the past decade. Inflation indexed bonds are typically issued by sovereign entities. The main issuers by outstanding volume are the US, UK, French and Italian Governments, but other European countries, Japan, Australia and Canada have also issued increasing amounts of inflation indexed bonds. The UK Debt Management Office reports that the market value of international inflation indexed government bonds has grown from about £500 mn in January 2003 to over £1,000 mn in June 2007. The success of inflation indexed bonds seems to be due to investors' desire to protect their long-term retirement savings from the dangers of inflation. Pension funds find inflation indexed bonds attractive to match their long-term liabilities. Inflation indexed bonds can be viewed and valued as inflation derivative securities, but they are not the only inflation derivatives. Recently proper inflation derivatives markets have developed in the US and the UK. The payoffs to these derivatives are linked to some measure of realized inflation, such as the UK's Retail Price Index (RPI) or the US's Consumer Price Index (CPI). Common inflation derivatives comprise Zero Coupon Inflation Indexed Swaps (ZCIIS), Year-on-Year Inflation Indexed Swaps (YYIIS) and inflation indexed options.

The main contribution of this paper is a tractable valuation model for pricing these inflation indexed bonds and derivatives in a closed form. The valuation model assumes a realistic process for the inflation rate and some model variants guarantee a strictly non-negative nominal interest rate. In particular closed-form solutions for inflation indexed bonds and derivatives are available even when the short-term nominal interest rate follows a squared Gaussian process as in Ahn et al. (2002).

Derivatives Market Journal, Inflation Indexed Bonds, Gaussian Model, Retail Price Index, Closed-Form Solutions, Debt Management Office, Consumer Price Index, CPI, Zero Coupon Inflation Indexed Swaps, ZCIIS, Year-on-Year Inflation Indexed Swaps, YYIIS, LIBOR Market Model Framework, Inflation Indexed Derivatives, European Type Inflation Options, Econometric Models, Risk Management.