Extensions of the Jarrow-Yildirim Inflation Model

Details

Supervisors

Devolder, Pierre ; Chatelain, Catherine

Faculty

Faculté des sciences

Degree label

Master [120] en sciences actuarielles, à finalité spécialisée

Abstract

This master's thesis aims to explore inflation modeling through an analysis of the classical Jarrow-Yildirim inflation model and two extensions of it: a G2++ and a Heston extension. As explicit pricing formulas for classical inflation-indexed products are available under the Jarrow-Yildirim model, we aim to price such products under these two extensions, including year-on-year inflation-indexed swaps, inflation-indexed caplets/floorlets, and caps/floors. The G2++ model, yielding closed-form expressions, is calibrated and its performance is compared to the calibration results obtained with the Jarrow-Yildirim model. We conclude with an actuarial application, utilising the calibrated models to price inflation-indexed life annuities. We delve into the significance of these products, demonstrate the derivation of closed pricing formulas through the concept of foreign currency analogy, and explore different product variations. Additionally, we analyse the relevance of employing the G2++ inflation model extension over the classical Jarrow-Yildirim model in this context.