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First Passage Times For Risk-Tracking Proxies

Author

Listed:
  • VICTOR VAUGIRARD

    (TEAM-CNRS, University of Paris-I Pantheon-Sorbonne, Maison des Sciences Economiques, 106-112 Boulevard de l'Hôpital, F-75013 Paris, France)

Abstract

This paper determines first passage time distributions with a two-fold emphasis. The focus is first set on interest rate randomness. It derives a closed-form solution in the case of moving boundaries, indexed on risk-free bonds, and where interest rates obey mean-reverting processes and underlyings follow lognormal diffusion processes. It turns next to the underlyings, which may not be exchange-traded and whose dynamics obey jump-diffusion processes. It builds an equilibrium valuation framework and determines the rational-expectations equilibrium price of digital options. As those underlyings may be risk-tracking indices, the article can be applied to pricing insurance-linked securities, such as catastrophe bonds.

Suggested Citation

  • Victor Vaugirard, 2005. "First Passage Times For Risk-Tracking Proxies," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 8(04), pages 445-462.
    • Handle: RePEc:wsi:ijtafx:v:08:y:2005:i:04:n:s0219024905003128
    DOI: 10.1142/S0219024905003128
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