Inflation Models with Correlation and Skew

TL;DR

This paper introduces a multi-factor inflation index model with correlation and skew, providing analytical pricing formulas and a simplified calibration method, demonstrated with market data.

Contribution

It develops a flexible multi-factor inflation model with correlation and skew, including a simplified calibration approach, applicable to various interest rate models.

Findings

Analytical formulas for swaps, caps, and floors prices.

Model effectively captures market volatility skew.

Simplified calibration method reduces computational effort.

Abstract

We formulate a forward inflation index model with multi-factor volatility structure featuring a parametric form that allows calibration to correlations between indices of different tenors observed in the market. Assuming the nominal interest rate follows a single factor Gaussian short rate model, we present analytical prices for zero-coupon and year-on-year swaps, caps, and floors. The same method applies to any interest rate model for which one can compute the zero-coupon bond prices and measure shifts. We extend the multi-factor model with leverage functions to capture the entire market volatility skew with a single process. The time-consuming calibration step of this model can be avoided in the simplified model that we further propose. We demonstrate the leveraged and the simplified models with market data.