A New Paradigm for Inflation Derivatives Modeling

In this chapter, we define the “inflation forward rates” based on arbitrage arguments and develop a dynamic model for the term structure of inflation forward rates. This new model can serve as a framework for specific no-arbitrage models, including the popular practitioners’ market model and all models based on “foreign currency analogy.” With our rebuilt market model, we can price inflation caplets, floorlets, and swaptions with the Black formula for displaced-diffusion processes, and thus can quote these derivatives using “implied Black's volatilities.” The rebuilt market model also serves as a proper platform for developing models to manage volatility smile risks. Through this chapter, we hope to correct two major flaws in existing models or with the current practices. First, a consumer price index has no volatility, so models based on the diffusion of the index are essentially wrong. Second, the differentiation of models based on zero-coupon inflation-indexed swaps and models based on year-on-year inflation-indexed swaps is unnecessary, and the use of “convexity adjustment,” a common practice to bridge models that are based on the two kinds of swaps, is redundant.