FIRST PASSAGE TIMES FOR RISK-TRACKING PROXIES

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

International Journal of Theoretical and Applied Finance (IJTAF), 2005, vol. 08, issue 04, 445-462

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.

Keywords: Hitting time; soft barrier; time change; jump-diffusion; shadow price (search for similar items in EconPapers)
Date: 2005
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DOI: 10.1142/S0219024905003128

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