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

TL;DR

This paper systematically explores alternative one-factor Cheyette model variants to improve the calibration of the 1-year caplet smile, extending the PDML framework and leveraging a generic scripting environment (GenSimFW) to enable flexible pricing and calibration. It compares piecewise-linear forward-rate local volatility (PwLinBRLV) with uncorrelated CIR SV, linear Cheyette-factor LV (LinXLV) with correlated QDLNSV, and other combinations, using both code-generated MC pricers and PDML surrogates. Key findings show that PwLinBRLV+CIRSV and LinXLV+QDLNSV (and related QDLNSV variants) can calibrate the 1-year smile well across strikes, while benchmark-forward formulations generally facilitate calibration; the study demonstrates that the proposed generic frameworks support efficient, robust calibration across maturities and model settings. The work highlights practical implications for producing fast, adaptable caplet pricing and calibration tools in multi-curve interest-rate environments, with potential for production-ready model development.

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

Figures (14)

• Figure 1: Calibrating the 1yr Maturity Caplet smile, Cheyette Model with Linear Benchmark Forward Rate Local Volatility and CIR SV. Figure and data from PDML. Shown is difference between model price (MC) and market price (MKT), MC error bars are shown for comparison.
• Figure 2: Script for Caplet Pricing for Cheyette Model with uncorrelated CIR SV (Euler for Cheyette, Euler full truncation for CIR), with piece-wise linear benchmark forward rate local volatility (PwLinBRLV).
• Figure 3: Script for Caplet Pricing for Cheyette Model with Lognormal SV with quadratic drift (Euler for both Cheyette and QDLNSV) with local volatility linear in the Cheyette factor $x$ (LinXLV).
• Figure 4: GenSimFW modes
• Figure 5: Calibration with Parametric Pricers