{"title":"A LÉVY-DRIVEN ORNSTEIN–UHLENBECK PROCESS FOR THE VALUATION OF CREDIT INDEX SWAPTIONS","authors":"YOSHIHIRO SHIRAI","doi":"10.1142/s021902492350022x","DOIUrl":null,"url":null,"abstract":"<p>A Lévy-driven Ornstein–Uhlenbeck process is proposed to model the evolution of the risk-free rate and default intensities for the purpose of evaluating option contracts on a credit index. Time evolution in credit markets is assumed to follow a gamma process in order to reflect the different speed at which credit products are exchanged with respect to securities, such as Treasuries, deemed risk-free. Formulas for the characteristic function, zero coupon bonds, moments of the process and its stationary distribution are derived. Numerical experiments showing convergence of standard numerical methods for the valuation PIDE to analytical and Monte Carlo solutions are shown. Calibration to market prices of options on a credit index is performed, and model- and market-implied summary statistics for the underlying credit spreads are estimated and compared.</p>","PeriodicalId":47022,"journal":{"name":"International Journal of Theoretical and Applied Finance","volume":"17 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2024-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Theoretical and Applied Finance","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/s021902492350022x","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"BUSINESS, FINANCE","Score":null,"Total":0}
引用次数: 0
Abstract
A Lévy-driven Ornstein–Uhlenbeck process is proposed to model the evolution of the risk-free rate and default intensities for the purpose of evaluating option contracts on a credit index. Time evolution in credit markets is assumed to follow a gamma process in order to reflect the different speed at which credit products are exchanged with respect to securities, such as Treasuries, deemed risk-free. Formulas for the characteristic function, zero coupon bonds, moments of the process and its stationary distribution are derived. Numerical experiments showing convergence of standard numerical methods for the valuation PIDE to analytical and Monte Carlo solutions are shown. Calibration to market prices of options on a credit index is performed, and model- and market-implied summary statistics for the underlying credit spreads are estimated and compared.
期刊介绍：
The shift of the financial market towards the general use of advanced mathematical methods has led to the introduction of state-of-the-art quantitative tools into the world of finance. The International Journal of Theoretical and Applied Finance (IJTAF) brings together international experts involved in the mathematical modelling of financial instruments as well as the application of these models to global financial markets. The development of complex financial products has led to new challenges to the regulatory bodies. Financial instruments that have been designed to serve the needs of the mature capitals market need to be adapted for application in the emerging markets.
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