{"title":"针对短期限胶囊校准的不同单因子切耶特模型案例研究","authors":"Arun Kumar Polala, Bernhard Hientzsch","doi":"arxiv-2408.11257","DOIUrl":null,"url":null,"abstract":"In [1], we calibrated a one-factor Cheyette SLV model with a local volatility\nthat is linear in the benchmark forward rate and an uncorrelated CIR stochastic\nvariance to 3M caplets of various maturities. While caplet smiles for many\nmaturities could be reasonably well calibrated across the range of strikes, for\ninstance the 1Y maturity could not be calibrated well across that entire range\nof strikes. Here, we study whether models with alternative local volatility\nterms and/or alternative stochastic volatility or variance models can calibrate\nthe 1Y caplet smile better across the strike range better than the model\nstudied in [1]. This is made possible and feasible by the generic simulation,\npricing, and calibration frameworks introduced in [1] and some new frameworks\npresented in this paper. We find that some model settings calibrate well to the\n1Y smile across the strike range under study. In particular, a model setting\nwith a local volatility that is piece-wise linear in the benchmark forward rate\ntogether with an uncorrelated CIR stochastic variance and one with a local\nvolatility that is linear in the benchmark rate together with a correlated\nlognormal stochastic volatility with quadratic drift (QDLNSV) as in [2]\ncalibrate well. We discuss why the later might be a preferable model. [1] Arun Kumar Polala and Bernhard Hientzsch. Parametric differential machine\nlearning for pricing and calibration. arXiv preprint arXiv:2302.06682 , 2023. [2] Artur Sepp and Parviz Rakhmonov. A Robust Stochastic Volatility Model for\nInterest Rate Dynamics. Risk Magazine, 2023","PeriodicalId":501084,"journal":{"name":"arXiv - QuantFin - Mathematical Finance","volume":"3 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A case study on different one-factor Cheyette models for short maturity caplet calibration\",\"authors\":\"Arun Kumar Polala, Bernhard Hientzsch\",\"doi\":\"arxiv-2408.11257\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In [1], we calibrated a one-factor Cheyette SLV model with a local volatility\\nthat is linear in the benchmark forward rate and an uncorrelated CIR stochastic\\nvariance to 3M caplets of various maturities. While caplet smiles for many\\nmaturities could be reasonably well calibrated across the range of strikes, for\\ninstance the 1Y maturity could not be calibrated well across that entire range\\nof strikes. Here, we study whether models with alternative local volatility\\nterms and/or alternative stochastic volatility or variance models can calibrate\\nthe 1Y caplet smile better across the strike range better than the model\\nstudied in [1]. This is made possible and feasible by the generic simulation,\\npricing, and calibration frameworks introduced in [1] and some new frameworks\\npresented in this paper. We find that some model settings calibrate well to the\\n1Y smile across the strike range under study. In particular, a model setting\\nwith a local volatility that is piece-wise linear in the benchmark forward rate\\ntogether with an uncorrelated CIR stochastic variance and one with a local\\nvolatility that is linear in the benchmark rate together with a correlated\\nlognormal stochastic volatility with quadratic drift (QDLNSV) as in [2]\\ncalibrate well. We discuss why the later might be a preferable model. [1] Arun Kumar Polala and Bernhard Hientzsch. Parametric differential machine\\nlearning for pricing and calibration. arXiv preprint arXiv:2302.06682 , 2023. [2] Artur Sepp and Parviz Rakhmonov. A Robust Stochastic Volatility Model for\\nInterest Rate Dynamics. Risk Magazine, 2023\",\"PeriodicalId\":501084,\"journal\":{\"name\":\"arXiv - QuantFin - Mathematical Finance\",\"volume\":\"3 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-08-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - QuantFin - Mathematical Finance\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2408.11257\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - QuantFin - Mathematical Finance","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.11257","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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