Inflation-indexed swaps and swaptions

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 a 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 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.