Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
권호 표지
DOI QR코드

DOI QR Code

ANALYTIC SOLUTIONS FOR AMERICAN PARTIAL BARRIER OPTIONS BY EXPONENTIAL BARRIERS

  • Bae, Chulhan (NICE P&I Inc) ;
  • Jun, Doobae (Department of Mathematics and Research Institute of Natural Science Gyeongsang National University)
  • Received : 2017.06.01
  • Accepted : 2017.06.06
  • Published : 2017.06.30
Download PDF
⟨ Previous Next ⟩

Abstract

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 Ku [10] where the exercise policies are constant.

Keywords

References

  1. M. Broadie and J. Detemple, American option valuation: new bounds, approx-imations, and a comparison of existing, Review of Financial Studies. 9 (1996) 1211-1250. https://doi.org/10.1093/rfs/9.4.1211
  2. M. J. Brennan and E. S. Schwartz, Savings bonds, retractable bonds and callable bonds, Journal of Financial Economics. 5 (1977) 67-88. https://doi.org/10.1016/0304-405X(77)90030-7
  3. P. Carr, R. Jarrow, and R. Myneni, Alternative characterization of American put options, Mathematical Finance. 2 (1992) 87-106. https://doi.org/10.1111/j.1467-9965.1992.tb00040.x
  4. J. C. Cox, S. A. Ross, and M. Rubinstein, Option pricing:A simplified approach, Journal of financial Economics. 7 (1979) 229-264. https://doi.org/10.1016/0304-405X(79)90015-1
  5. 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. https://doi.org/10.1016/S0165-1889(99)00093-7
  6. R. C. Heynen and H. M. Kat, Partial barrier options, The Journal of Financial Engineering. 3 (1994) 253-274.
  7. J. Ingersoll, Approximating American options and other financial contracts using barrier derivatives, Journal of Computational Finance. 2 (1998) 85-112. https://doi.org/10.21314/JCF.1998.019
  8. S. D. Jacka, Optimal stopping and the American put, Mathematical Finance. 1 (1991) 1-14.
  9. 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.
  10. D. Jun and H. Ku, Valuation of American partial barrier options, Review of Derivatives Research. 16 (2013) 167-191. https://doi.org/10.1007/s11147-012-9081-1
  11. I. J. Kim, The analytic valuation of American options, Review of financial stud-ies. 3 (1990) 547-572. https://doi.org/10.1093/rfs/3.4.547
  12. 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. https://doi.org/10.1080/14697688.2012.696780
  13. 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. https://doi.org/10.1007/s00211-007-0091-0
  14. F. A. Longsta and E. S. Schwartz, Valuing American options by simulation:a simple least-squares approach, Review of Financial studies. 14 (2001) 113-147. https://doi.org/10.1093/rfs/14.1.113
  15. M. Parkinson, Option pricing:the American put, The Journal of Business. 50 (1977) 21-36. https://doi.org/10.1086/295902
  16. M. A. Sullivan, Valuing American put options using Gaussian quadrature. The Review of Financial Studies 13 (2000), 75-94. https://doi.org/10.1093/rfs/13.1.75