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

TL;DR

This paper compares different one-factor Cheyette models with various local and stochastic volatility terms to improve calibration of 1Y caplet smiles across strike ranges, building on previous frameworks.

Contribution

It introduces and tests alternative local volatility and stochastic volatility models within a unified calibration framework for better 1Y caplet smile fitting.

Findings

Certain model configurations calibrate well across strike ranges.

Piece-wise linear local volatility with uncorrelated CIR variance performs well.

Linear local volatility with correlated QDLNSV is potentially preferable.

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