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This is a survey on American options. An American option allows its owner the privilege of early exercise, whereas a European option can be exercised only at expiration. Because of this early exercise privilege American option pricing involves an optimal stopping problem; the price of an American option is given as a free boundary value problem associated with a Black-Scholes type partial differential equation. Up until now there is no simple closed-form solution to the problem, but there have been a variety of approaches which contribute to the understanding of the properties of the price and the early exercise boundary. These approaches typically provide numerical or approximate analytic methods to find the price and the boundary. Topics included in this survey are early approaches(trees, finite difference schemes,and quasi-analytic methods), an analytic method of lines and randomization, a homotopy method, analytic approximation of early exercise boundaries, Monte Carlo methods, and relatively recent topics such as model uncertainty, backward stochastic differential equations, and real options. We also provide open problems whose answers are expected to contribute to American option pricing.
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참고문헌 (30)
참고문헌 신청
A. Bensoussan / 1984 / On the theory of option pricing / Acta Appl. Math 2 (2) : 139 ~ 158
A. Dixit / 1994 / Investment Under Uncertainty / Princeton University Press
B. Gao / 2000 / The valuation of American barrier options using the decomposition technique / J. Econom. Dynam. Control 24 : 1783 ~ 1827
C. Ahn / 2009 / A LONG TIME ASYMPTOTIC BEHAVIOR OF THE FREE BOUNDARY FOR AN AMERICAN PUT / Proceedings Of The American Mathematical Society 137 (10) : 3425 ~ 3436
D. A. Bunch / 2000 / The American put option and its critical stock price / Journal of Finance 55 : 2333 ~ 2356
A. Dixit / 1994 / Investment Under Uncertainty / Princeton University Press
B. Gao / 2000 / The valuation of American barrier options using the decomposition technique / J. Econom. Dynam. Control 24 : 1783 ~ 1827
C. Ahn / 2009 / A LONG TIME ASYMPTOTIC BEHAVIOR OF THE FREE BOUNDARY FOR AN AMERICAN PUT / Proceedings Of The American Mathematical Society 137 (10) : 3425 ~ 3436
D. A. Bunch / 2000 / The American put option and its critical stock price / Journal of Finance 55 : 2333 ~ 2356
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