Paper: arXiv 2405.05101

Authors: Orcan Ogetbil, Bernhard Hientzsch

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.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 6.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a strong theoretical framework for inflation modeling, incorporating multi-factor volatility and local stochastic leverage functions to capture skew. It demonstrates solid quantitative rigor by providing analytical pricing formulas for inflation derivatives and validating calibration using market data.

Research Flowchart

  flowchart TD
    A[Goal: Model Forward Inflation Index with Correlation & Volatility Skew] --> B[Input: Market Data & Nominal Interest Rates]
    B --> C[Formulate Multi-Factor Volatility Model with Parametric Correlation]
    C --> D[Derive Analytical Pricing for Swaps, Caps, & Floors]
    D --> E[Extend with Leverage Functions for Volatility Skew]
    E --> F[Develop Simplified Model to Avoid Time-Consuming Calibration]
    F --> G[Outcomes: Fast Calibration & Accurate Pricing across Inflation Tenors]

Cited References (8)

  1. A Quadratic Gaussian Year-on-Year Inflation Model (2013) — link
  2. Pricing inflation-indexed derivatives (2005) — link
  3. Calibration Methods of Hull-White Model (2009) — link
  4. Interest rate models, inflation-based derivatives, trigger notes and cross-currency swaptions (2000)
  5. Risk Neutral Valuation of Inflation-Linked Interest Rate Derivatives (2019) — link
  6. Extensions of Dupire Formula: Stochastic Interest Rates and Stochastic Local Volatility (2023) — link
  7. CALIBRATING LOCAL VOLATILITY MODELS WITH STOCHASTIC DRIFT AND DIFFUSION (2022) — link
  8. Markov models for commodity futures: theory and practice (2010) — link

0 of 8 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.