Optimal stopping, free boundary, and American option in a jump-diffusion model |
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Authors: | Huyên Pham |
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Institution: | (1) CEREMADE, Université Paris IX Dauphine, Place du Maréchal de Lattre de Tassigny, 75775 Paris Cedex, France;(2) CREST, Laboratoire de Finance-Assurance, 15 boulevard Gabriel Péri, 92245 Malakoff Cedex, France;(3) Present address: Equipe d’Analyse et de Mathématiques Appliquées, Université de Marne la Vallée, 2 rue de la Butte verte, 93166 Noisy le Grand cedex, France |
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Abstract: | This paper considers the American put option valuation in a jump-diffusion model and relates this optimal-stopping problem
to a parabolic integro-differential free-boundary problem, with special attention to the behavior of the optimal-stopping
boundary. We study the regularity of the American option value and obtain in particular a decomposition of the American put
option price as the sum of its counterpart European price and the early exercise premium. Compared with the Black-Scholes
(BS) 5] model, this premium has an additional term due to the presence of jumps. We prove the continuity of the free boundary
and also give one estimate near maturity, generalizing a recent result of Barleset al. 3] for the BS model. Finally, we study the effect of the market price of jump risk and the intensity of jumps on the American
put option price and its critical stock price. |
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Keywords: | Optimal stopping Jump-diffusion model American option Free-boundary problem |
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