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A Lã‰Vy-Driven Ornstein–Uhlenbeck Process For The Valuation Of Credit Index Swaptions

Author

Listed:
  • YOSHIHIRO SHIRAI

    (Department of Mathematics, University of Maryland, College Park, MD 20742, USA)

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.

Suggested Citation

  • Yoshihiro Shirai, 2023. "A Lã‰Vy-Driven Ornstein–Uhlenbeck Process For The Valuation Of Credit Index Swaptions," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 26(06n07), pages 1-37, November.
    • Handle: RePEc:wsi:ijtafx:v:26:y:2023:i:06n07:n:s021902492350022x
    DOI: 10.1142/S021902492350022X
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