针对短期限胶囊校准的不同单因子切耶特模型案例研究

Arun Kumar Polala, Bernhard Hientzsch
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摘要

在文献[1]中,我们校准了一个单因子 Cheyette SLV 模型,该模型具有与基准远期利率线性相关的局部波动率和不相关的 CIR 随机方差,可以校准不同期限的 3M caplet。虽然许多到期日的小盘收益率都能在一定范围内得到合理的校准,但例如 1Y 到期日的小盘收益率就不能在一定范围内得到很好的校准。在这里,我们研究了具有替代性局部波动率术语和/或替代性随机波动率或方差模型的模型是否能比 [1] 中研究的模型更好地校准 1Y 的 caplet smile。本文[1]中引入的通用模拟、定价和校准框架以及本文提出的一些新框架使这一点成为可能和可行。我们发现,在研究的打击范围内,一些模型设置能很好地校准 1Y smile。特别是,本文[2]中的局部波动率与基准远期利率成片断线性关系、随机方差为非相关 CIR 的模型设置,以及局部波动率与基准利率成线性关系、随机方差为二次漂移(QDLNSV)的相关对数正态分布的模型设置,都能很好地校准。我们将讨论为什么后一种模型更可取。[1] Arun Kumar Polala 和 Bernhard Hientzsch.ArXiv preprint arXiv:2302.06682 , 2023.[2] Artur Sepp and Parviz Rakhmonov.利率动态的稳健随机波动模型》。风险杂志,2023 年
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A case study on different one-factor Cheyette models for short maturity caplet calibration
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
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