Pricing of contingent claims in a two-dimensional model with random dividends * Pavel V. Gapeev † Monique Jeanblanc ‡ CDAM Research Report LSE-CDAM-2008-07 (18 pp) We study a model where two assets are paying dividends with rates changing from one fixed value to another when any credit event occurs. The credit events are associated with the first times when the asset values fall to some given constant levels. The behavior of asset values is described by exponential diffusion processes with random drift rates and independent driving Brownian motions. We obtain closed form expressions for the ex-dividend prices of certain barrier-type contingent claims with structure similar to first- and second-to-default options in credit risk theory. 1 Introduction One of the known advantages of structural modeling is the explicit form of the credit events that are associated with the passage times of the related asset value processes on some given * This research benefited from the support of the ’Chaire Risque de Cr´ edit’, F´ ed´ eration Bancaire Fran¸ caise. † London School of Economics, Department of Mathematics, Houghton Street, London WC2A 2AE, United Kingdom; e-mail: p.v.gapeev@lse.ac.uk (supported by ESF AMaMeF Short Visit Grant 1356) ‡ Universit´ e d’Evry Val d’Essonne, D´ epartement de Math´ ematiques, rue Jarlan, F-91025 Evry Cedex, France; Europlace Institute of Finance; e-mail: monique.jeanblanc@univ-evry.fr Mathematics Subject Classification 2000: Primary 91B70, 60J60, 60G40. Secondary 91B28, 60J25. Key words and phrases: Structural approach, Brownian motion, running minimum process, first passage time, random dividend rates, dependent credit events, first- and second-to-default options, strong Markov property, full and partial information. Date: June 18, 2008 1