Inflation-rate Derivatives: From Market Model to Foreign Currency Analogy

TL;DR

This paper develops a market model for inflation rate derivatives, connecting it to foreign currency analogy, and extends it to handle volatility smiles, providing a unified framework for pricing and modeling inflation derivatives.

Contribution

It introduces a market model for inflation derivatives based on risk-neutral bond dynamics and links it to foreign currency models, extending to volatility smile considerations.

Findings

Pricing formulas similar to Black's formula for inflation options

Extension of the model to incorporate volatility smiles

Re-derivation of Jarrow and Yildirim's model using foreign currency analogy

Abstract

In this paper, we establish a market model for the term structure of forward inflation rates based on the risk-neutral dynamics of nominal and real zero-coupon bonds. Under the market model, we can price inflation caplets as well as inflation swaptions with a formula similar to the Black's formula, thus justify the current market practice. We demonstrate how to further extend the market model to cope with volatility smiles. Moreover, we establish a consistency condition on the volatility of real zero-coupon bonds using arbitrage arguments, and with that re-derive the model of Jarrow and Yildirim (2003) with real forward rates based on "foreign currency analogy", and thus interconnect the two modeling paradigms.