Posted: November 12th, 2024

Pricing Inflation-Indexed Derivatives Using the Extended Vasicek Model of Hull and White

Pricing Inflation-Indexed Derivatives Using the Extended Vasicek Model of Hull and White

The purpose of this thesis is to review the framework for pricing inflation-indexed derivatives using the two currency Heath-Jarrow-Morton approach introduced by Yildirim and Jarrow and to derive prices for the most commonly traded inflation-indexed derivatives using the HullWhite model.

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The first chapter gives an overview of the inflation markets and gives a brief description of the securities that are traded and their liquidity in the major markets. Some of the considerations peculiar to the inflation-indexed markets such as seasonality and indexation are then reviewed. The second chapter provides the mathematical background for the model. Gaussian Markov short-rate models are described in the HJM framework and the restrictions on the HJM volatility structure that allow the dynamics to be represented by a Markovian short rate model are described. The dynamics of the zero-coupon bond in the single currency setting is then derived in terms of the short rate parameters. The real economy is then introduced in terms of the economy of the foreign currency and the martingale measure is constructed for the extended set of nominal tradables.

The third chapter describes the most popular inflation-indexed derivative securities in more detail and in particular derives prices for year-on-year inflation-indexed swaps and inflation-indexed caps and floors using the model. The fourth chapter describes calibration considerations. In particular it reviews how the most popular nominal derivatives such as swaptions and caps/floors can be expressed in terms of options on zero-coupon bonds and hence how they can be priced using the dynamics of the zero-coupon bond that were derived in the second chapter. A simple approach to calibrating the inflation model is also described.

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