 A LÉVY-DRIVEN ORNSTEIN–UHLENBECK PROCESS FOR THE VALUATION OF CREDIT INDEX SWAPTIONSInternational Journal of Theoretical and Applied Finance (IJTAF), 2023, vol. 26, issue 06n07, 1-37 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. Keywords: Lévy-driven OU processes; self-decomposability; multiple gamma processes; credit index swaptions; credit spreads (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:wsi:ijtafx:v:26:y:2023:i:06n07:n:s021902492350022x Ordering information: This journal article can be ordered from DOI: 10.1142/S021902492350022X Access Statistics for this article International Journal of Theoretical and Applied Finance (IJTAF) is currently edited by L P Hughston More articles in International Journal of Theoretical and Applied Finance (IJTAF) from World Scientific Publishing Co. Pte. Ltd. |
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