Pricing Treasury Inflation Protected Securities and Related Derivatives using an HJM Model

We introduce a new approach to model the market smile for inflationlinked derivatives by defining the Quadratic Gaussian Year-on-Year inflation model-the QGY model. We directly define the model in terms of a year-onyear ratio of the inflation index on a discrete tenor structure, which, along with the nominal discount bond, is driven by a log-quadratic function of a multi-factor Gaussian Markov process.We find closed-form expressions for the drift of the inflation index and for inflation-linked swaps. We get a Black-Scholes-type pricing formula for year-on-year inflation caplets in semi-analytical form. The formula contains an integral of a multivariate Gaussian density over a quadratic domain. In a two-dimensional case, we show how this integral reduces to a one-dimensional integration along the boundary of a conic section.In the case where the year-on-year inflation ratio is driven by two factors, we specify a spherical parameterisation. This gives an intuitive control over the curvature and the skew of the year-on-year inflation smile and shows the maximum curvature and skew obtainable with a particular three-factor version of the QGY model. Within this three-factor model, we identify a parameterisation to control the autocorrelation structure of the inflation index.We calibrate the model to year-on-year inflation options on the UK's Retail Prices Index (RPI) and the eurozone's Harmonised Index of Consumer Prices Excluding Tobacco (HICPxT) and get a good fit to the smile of implied volatilities. We use the calibrated model to price HICPxT zero-coupon inflation options and RPI limited price indices (LPIs). Furthermore, we provide methods to interpolate the process for the inflation index and the year-on-year inflation ratio between dates on the tenor structure.

Section: Inflation Modelsmentioning

confidence: 99%

Section: Jarrow-yıldırım Inflation Model and Extensionsmentioning

confidence: 99%

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A Quadratic Gaussian Year-on-Year Inflation Model

Gretarsson

2013

“…The pricing of Inflation derivatives cannot be made without a model for the nominal discount curve. Classic approaches such as [11] model inflation as the exchange rate between the nominal and the real economy, instead we model inflation directly as a traded asset. Though this assumption is inconsistent with market reality 2 , it leads to very similar formulae for ZCIIS prices.…”

Section: A Factorial Model For Inflationmentioning

confidence: 99%

Cross-Hedging of Inflation Derivatives on Commodities: The Informational Content of Futures Markets

Fulli-Lemaire¹,

Palidda²

2013

According to the macro-econometric literature, the impact of exogenous oil price shocks on Inflation have greatly increased in the last two decades throughout OECD countries while the persistence of those shocks on long-term inflation, namely core inflation, has dramatically decreased. In the meantime, the market for inflation derivatives soared, spurred by a revival of the primary inflation-linked bond market. As the contribution of core inflation to the total headline inflation volatility bottomed, most of the volatility of headline inflation should thus be explained by changes in the spread between headline and core inflation indicators: a factor closely linked to commodity markets. This economic analysis should have important financial arbitrage implications in the futures market: are exogenous shocks on oil futures markets incorporated into zero coupon inflation indexed swap prices? To investigate this issue, we propose on the one hand a four-factor model for both inflation and nominal rates, and on the other hand a two-factor model for commodities. We proceed to an empirical estimation of the model using prices of oil futures contracts and inflation breakeven rates from which we can in particular extract a synthetic core inflation forward curve.

“…Many studies investigated and supported the use of inflation-linked bonds to monitor inflation expectations. Among others, we can cite Hetzel (1992), Breedon (1995), Campbell and Shiller (1996), Deacon and Andrews (1996), Barr and Campbell (1997), Kitamura (1997), Evans (1998), Emmons (2000), Jarrow and Yildirim (2003), Bernanke (2004), Buraschi and Jiltsov (2005), Hordahl et al (2005), Liu and Cheng (2005), D'Amico et al (2006), Ang et al (2007), Garcia and van Rixtel (2007), Haubrich et al (2008) and Grishenko and Huang (2010).…”

Section: Introductionmentioning

confidence: 99%

Break-Even Inflation Rate and the Risk Premium: An Alternative Approach to the VAR Models in Forecasting the CPI

Furlani

2011

This paper examines, for the Brazilian case, if break-even inflation rates (BEIR) extracted from fixed income securities is an unbiased estimator of consumer inflation, measured by the CPI. Our estimates suggest that BEIRs are informative about future inflation, especially for the maturity of three months. The main innovation of our work, however, is the method used for estimation, allowing us to conclude that the inflation risk premium, for some maturities considered, varies over time and is not irrelevant from the economic standpoint.We also compared the inflation forecasts obtained from BEIRs with the ones extracted from VAR models used by Central Bank and estimates from the Focus Survey Report's Top5s.The forecasts performed with BEIRs showed greater accuracy than those extracted from VAR models. These projections, however, underperformed those from the Top5s.JEL Classification: E31, E43, E44.