Inflation Indexed Swaps and Swaptions

This article considers the pricing of inflation indexed swaps, 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 a general marked point process. Our model is an extension of the HJM approach proposed by Jarrow and Yildirim (2003) and later also used by Mercurio (2005) to price inflation indexed swaps. Furthermore
we price options on so called TIPS-bonds assuming the model is purely Wiener driven. We then introduce an 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 earlier used by Hughston (1998), Jarrow & Yildirim (2003) and Mercurio (2005).