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Reconciling Year on Year and Zero Coupon Inflation Swap: A Market Model Approach

7 Pages Posted: 1 Sep 2004 Last revised: 10 Dec 2007

Nabyl Belgrade

CDC Ixis Capital Markets

Eric Benhamou

Université Paris Est - Université Paris Est-Creteil

Date Written: August 2004

Abstract

Despite the recent growth of inflation linked derivatives market, the publicly available literature is very small. The various macro econometrics models are helpless when it comes to pricing inflation derivatives. The only freely accessible model, the Jarrow and Yildirim [4], relies on non observable data such as real yields. This makes this model hard to calibrate. In addition, it does not provide simple connection between liquid instruments like year on year, zero coupon swap and the modeling of the corresponding CPI correlation. To fill this gap, we adapt a market model to inflation. This can be seen as a simple translation of the Libor market model to inflation. We see how volatilities of year on year, zero coupon swap and the integrated CPI correlation are related. Hence, out of the three, only two are independent and these two provide the latter. We derive an upper and lower bound for the non independent parameter leading to coherence tests. We conclude by convexity correction formula for year on year rates, emphasizing the impact of correlation between interest and inflation rates.

Keywords: Inflation derivatives, year on year, zero coupon swap, CPI, convexity correction

JEL Classification: G12, G31, M21

Suggested Citation

Belgrade, Nabyl and Benhamou, Eric, Reconciling Year on Year and Zero Coupon Inflation Swap: A Market Model Approach (August 2004). Available at SSRN: https://ssrn.com/abstract=583641 or http://dx.doi.org/10.2139/ssrn.583641

Nabyl Belgrade

CDC Ixis Capital Markets ( email )

47 quai d'Austerlitz
Paris, 75013
France
0033 (0)158551556 (Phone)

Eric Benhamou (Contact Author)

Université Paris Est - Université Paris Est-Creteil ( email )

61 avenue du Général de Gaulle
Créteil, 940000
France

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