On a martingale associated to generalized Ornstein–Uhlenbeck processes and an application to finance
نویسنده
چکیده
In this paper we study the two-dimensional joint distribution of the first passage time of a constant level by spectrally negative generalized Ornstein–Uhlenbeck processes and their primitive stopped at this first passage time. By using martingales techniques, we show an explicit expression of the Laplace transform of the distribution in terms of new special functions. Finally, we give an application in finance which consists of computing the Laplace transform of the price of an European call option on the maximum on the yield in the generalized Vasicek model. The stable case is studied in more detail. r 2004 Elsevier B.V. All rights reserved. MSC: primary 60G44; 60G40; 60G51; secondary 33C05; 91B70
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