Analytic solutions for American partial barrier options by exponential barriers

Chulhan Bae, Doobae Jun


This paper concerns barrier option of American type where the underlying price is monitored during only part of the option's life. Analytic valuation formulas of the American partial barrier options are obtained by approximation method. This approximation method is based on barrier options along with exponential early exercise policies. This result is an extension of Jun and [10] where the exercise policies are constant.


American option; partial barrier option; exponential barrier

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M. Broadie and J. Detemple, American option valuation: new bounds, approximations, and a comparison of existing, Review of Financial Studies. 9 (1996) 1211–1250.

M. J. Brennan and E. S. Schwartz, Savings bonds, retractable bonds and callable bonds, Journal of Financial Economics. 5 (1977) 67–88.

P. Carr, R. Jarrow, and R. Myneni, Alternative characterization of American put options, Mathematical Finance. 2 (1992) 87–106.

J. C. Cox, S. A. Ross, and M. Rubinstein, Option pricing:A simplified approach, Journal of financial Economics. 7 (1979) 229–264.

B. Gao, J. Huang, and M. Subrahmanyyam, The valuation of American barrier options using the decomposition technique, Journal of Economic Dynamics and Control. 24 (2000) 1783–1827.

R. C. Heynen and H. M. Kat, Partial barrier options, The Journal of Financial Engineering. 3 (1994) 253–274.

J. Ingersoll, Approximating American options and other financial contracts using barrier derivatives, Journal of Computational Finance. 2 (1998) 85–112.

S. D. Jacka, Optimal stopping and the American put, Mathematical Finance. 1 (1991) 1–14.

N. Ju, Pricing and American Option by Approximating Its Early Exercise Boundary as a Multipiece Exponential Function, The Review of Financial Stud- ies. (1998) 627–646.

D. Jun and H. Ku, Valuation of American partial barrier options, Review of Derivatives Research. 16 (2013) 167–191.

I. J. Kim, The analytic valuation of American options, Review of financial studies. 3 (1990) 547–572.

J. Kim, B. G. Jang, and K. T. Kim, A simple iterative method for the valuation of American options, Journal of Quantitative Finance. 13 (2013) 885–895.

J. Liang, B. Hu, L. Jiang, and B. Bian, On the rate of convergence of the binomial tree scheme for American options, Numerische Mathematik. 107 (2007) 333–352.

F. A. Longstaff and E. S. Schwartz, Valuing American options by simulation:a simple least-squares approach, Review of Financial studies. 14 (2001) 113–147.

M. Parkinson, Option pricing:the American put, The Journal of Business. 50 (1977) 21–36.

M. A. Sullivan, Valuing American put options using Gaussian quadrature. The Review of Financial Studies 13 (2000), 75–94.



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