Reconciling Year on Year and Zero Coupon Inflation Swap: A Market Model Approach
7 Pages Posted: 1 Sep 2004 Last revised: 10 Dec 2007
Date Written: August 2004
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 , 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: Suggested Citation