Abstract
This article considers the pricing and hedging of inflation-indexed swaps, and the pricing of inflation-indexed swaptions, and options on inflation-indexed bonds. To price the inflation-indexed swaps, we suggest an extended HJM model. The model allows both the forward rates and the consumer price index to be driven, not only by a standard Multidimensional Wiener process but also by I general marked point process. Our model is an extension of the HJM approach proposed by Jarrow and Yildirim [Jarrow, R., Yildirim Y., 2003. Pricing treasury inflation protected securities and related derivatives using an HJM model. Journal of Financial and Quantitative Analysis 38. 409-430] and later also used by Mercurio [Mercurio. F., 2005. Pricing inflation-indexed derivatives. Quantitative Finance 5 (3), 289-302] to price inflation-indexed swaps. Furthermore we price options on so called TIPS-bonds assuming the model is purely Wiener driven. We then introduce all inflation swap market model to price inflation-indexed swaptions. All prices derived have explicit closed-form solutions. Furthermore. we formally prove the validity of the so called foreign-currency analogy.