Optimal stopping, free boundary, and American option in a jump-diffusion model

被引：20
作者：
Pham H. [1 ,2 ,3 ]
机构：
[1] CEREMADE, Université Pans IX Dauphine, 75775 Paris Cedex, Pl. Marechal de Lattre de Tassigny
[2] CREST, Laboratoire de Finance-Assurance, 92245 Malakoff Cedex
[3] Equipe d'Analyse et de Mathématiques Appliquées, Université de Marne la Vallée, 93166 Noisy le Grand Cedex
来源：
Applied Mathematics and Optimization | 1997年 / 35卷 / 2期
关键词：
American option; Free-boundary problem; Jump-diffusion model; Optimal stopping;
D O I：
10.1007/BF02683325
中图分类号：
学科分类号：
摘要：
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 Barles et 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. © 1997 Springer-Verlag New York Inc.
引用
收藏
页码：145 / 164
页数：19
相关论文
共 33 条
  • [1] Aase K.K., Contingent Claims Valuation When the Security Price is a Combination of an Itô Process and a Random Point Process, Stochastic Process, Appl., 28, pp. 185-220, (1988)
  • [2] Ahn C.M., Thompson H.E., The Impact of Jump Risks on Nominal Interest Rates and Foreign Exchange Rates, Rev. Quant. Finan. Account., 2, pp. 17-31, (1992)
  • [3] Barles G., Burdeau J., Romano M., Samsoen N., Critical Stock Price Near Expiration, Math. Finan., 5, 2, pp. 77-95, (1995)
  • [4] Bensoussan A., Lions J.L., Applications des Inéquations Variationnelles en Contrôle Stochastique, (1978)
  • [5] Black F., Scholes M., The Pricing of Options and Corporate Liabilities, J. Polit. Econ., 81, pp. 637-659, (1973)
  • [6] Carr P., Jarrow R., Myneni R., Alternative Characterizations of American Put Options, Math. Finan., 2, pp. 87-106, (1992)
  • [7] Colwell D.B., Elliott R.J., Discontinuous Asset Prices and Non-Attainable Contingent Claims, Math. Finan., 3, 3, pp. 295-308, (1993)
  • [8] El Karoui N., Millet A., Lepeltier J.P., A Probabilistic Approach to the Réduite in Optimal Stopping, Probab. Math. Statist., 13, pp. 97-121, (1992)
  • [9] Friedman A., Parabolic Variational Inequalities in One Space Dimension and Smoothness of the Free Boundary, J. Funct. Anal., 18, pp. 151-176, (1975)
  • [10] Friedman A., Robin M., The Free Boundary for Variational Inequalities with Nonlocal Operators, SIAM J. Control Optim., 16, 2, pp. 347-372, (1978)
1234