A case study on different one-factor Cheyette models for short maturity caplet calibration

ArXiv ID: 2408.11257 “View on arXiv”

Authors: Unknown

Abstract

In [“1”], we calibrated a one-factor Cheyette SLV model with a local volatility that is linear in the benchmark forward rate and an uncorrelated CIR stochastic variance to 3M caplets of various maturities. While caplet smiles for many maturities could be reasonably well calibrated across the range of strikes, for instance the 1Y maturity could not be calibrated well across that entire range of strikes. Here, we study whether models with alternative local volatility terms and/or alternative stochastic volatility or variance models can calibrate the 1Y caplet smile better across the strike range better than the model studied in [“1”]. This is made possible and feasible by the generic simulation, pricing, and calibration frameworks introduced in [“1”] and some new frameworks presented in this paper. We find that some model settings calibrate well to the 1Y smile across the strike range under study. In particular, a model setting with a local volatility that is piece-wise linear in the benchmark forward rate together with an uncorrelated CIR stochastic variance and one with a local volatility that is linear in the benchmark rate together with a correlated lognormal stochastic volatility with quadratic drift (QDLNSV) as in [“2”] calibrate well. We discuss why the later might be a preferable model. [“1”] Arun Kumar Polala and Bernhard Hientzsch. Parametric differential machine learning for pricing and calibration. arXiv preprint arXiv:2302.06682 , 2023. [“2”] Artur Sepp and Parviz Rakhmonov. A Robust Stochastic Volatility Model for Interest Rate Dynamics. Risk Magazine, 2023

Keywords: Cheyette SLV Model, Calibration, Caplet Smile, Stochastic Volatility, Interest Rate Derivatives, Fixed Income / Interest Rates

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail
• Why: The paper is mathematically dense with detailed SDEs for various Cheyette and stochastic volatility models, while also providing empirical calibration results with specific parameters and comparison plots for caplet smiles.

  flowchart TD
    Goal["Research Goal<br>Improve calibration of 1Y caplet smile<br>using alternative Cheyette SLV models"] --> Inputs
    Inputs["Data / Inputs<br>1Y Caplet Market Data<br>Existing models from [1"]]
    Inputs --> Method
    Method["Methodology<br>Implement generic simulation & pricing frameworks<br>from [1"] + new frameworks from this paper]
    Method --> Models["Calibration Process<br>Test various model configurations:<br>- Linear LV + CIR (Benchmark)<br>- Piece-wise Linear LV + CIR<br>- Linear LV + QDLNSV [2"]]
    Models --> Results["Results & Findings"]
    Results{"Outcome"}
    Result1["Calibration Success"] --> Details1["Models with Piece-wise Linear LV + CIR<br>and Linear LV + QDLNSV<br>calibrate well across strike range"]
    Result2["Discussion"] --> Details2["QDLNSV model preferred<br>due to robustness & properties"]
    Outcome --> Result1
    Outcome --> Result2
    click Goal "Research Goal" "Research Goal"
    click Inputs "Data / Inputs" "Data / Inputs"
    click Method "Methodology" "Methodology"
    click Models "Calibration Process" "Calibration Process"
    click Result1 "Results / Findings" "Results / Findings"
    click Result2 "Results / Findings" "Results / Findings"
    linkStyle 0 stroke-width:2px,fill:none,stroke:black
    linkStyle 1 stroke-width:2px,fill:none,stroke:black
    linkStyle 2 stroke-width:2px,fill:none,stroke:black
    linkStyle 3 stroke-width:2px,fill:none,stroke:black
    linkStyle 4 stroke-width:2px,fill:none,stroke:blue
    linkStyle 5 stroke-width:2px,fill:none,stroke:blue
    linkStyle 6 stroke-width:2px,fill:none,stroke:black
    linkStyle 7 stroke-width:2px,fill:none,stroke:black