A correction note on the first passage time of an Ornstein-Uhlenbeck process to a boundary | Zendy

B. LeBlanc | Zendy; Olivier Renault | Zendy; Olivier Scaillet | Zendy

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A correction note on the first passage time of an Ornstein-Uhlenbeck process to a boundary

Author(s) -

B. LeBlanc,

Olivier Renault,

Olivier Scaillet

Publication year - 2000

Publication title -

finance and stochastics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.949

H-Index - 50

eISSN - 1432-1122

pISSN - 0949-2984

DOI - 10.1007/s007800050007

Subject(s) - ornstein–uhlenbeck process , mathematics , invariant measure , logarithm , boundary (topology) , measure (data warehouse) , mathematical finance , hitting time , expression (computer science) , invariant (physics) , stochastic process , mathematical analysis , statistical physics , mathematical physics , statistics , physics , computer science , economics , data mining , financial economics , ergodic theory , programming language

. This paper provides the derivation of the hitting time density of an Ornstein-Uhlenbeck process to a flat boundary. The derivation relies on a change of measure approach and delivers an explicit formula. This formula is an amended expression of the result given in Leblanc and Scaillet (1998). It corresponds to the formula given by a time substitution approach when the boundary level coincides with the mean of the invariant measure. It can for example be used to price digital up-and-in credit spread options when the logarithm of the credit spread is assumed to follow an Ornstein-Uhlenbeck process.

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