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Generalised Geske‐‐Johnson Interpolation of Option Prices

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  • San–Lin Chung
  • Mark B. Shackleton

Abstract

This paper describes four separate option types as special cases of Bermudans with general inter–exercise and time to final maturity. This produces a surface with European, finite American, infinite Bermudan and infinite American options as special cases. This allows Geske–Johnson (1984) two–point pricing to be extended to consider time–to–maturity as well as time–between–exercise opportunities. Due to their position on this ‘map’, infinite Bermudans are christened Arctic options and their pricing solution is presented. Numerical comparisons to benchmark methods are made for call prices under GBM although the results here hold for other processes and for both puts and calls when symmetry arguments are invoked.

Suggested Citation

  • San–Lin Chung & Mark B. Shackleton, 2007. "Generalised Geske‐‐Johnson Interpolation of Option Prices," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 34(5‐6), pages 976-1001, June.
    • Handle: RePEc:bla:jbfnac:v:34:y:2007:i:5-6:p:976-1001
    DOI: 10.1111/j.1468-5957.2007.02014.x
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    References listed on IDEAS

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    1. Sydney D. Howell & Axel J. Jägle, 1997. "Laboratory Evidence on How Managers Intuitively Value Real Growth Options," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 24(7&8), pages 915-935.
    2. Andrew W. Stark, 2000. "Real Options, (Dis)Investment Decision‐Making and Accounting Measures of Performance," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 27(3‐4), pages 313-331, April.
    3. Jing-Zhi Huang & Marti G. Subrahmanyam & G. George Yu, 1999. "Pricing And Hedging American Options: A Recursive Integration Method," World Scientific Book Chapters, in: Marco Avellaneda (ed.), Quantitative Analysis In Financial Markets Collected Papers of the New York University Mathematical Finance Seminar, chapter 8, pages 219-239, World Scientific Publishing Co. Pte. Ltd..
    4. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474.
    5. Johnson, H. E., 1983. "An Analytic Approximation for the American Put Price," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 18(1), pages 141-148, March.
    6. Barone-Adesi, Giovanni & Whaley, Robert E, 1987. "Efficient Analytic Approximation of American Option Values," Journal of Finance, American Finance Association, vol. 42(2), pages 301-320, June.
    7. Shackleton, Mark B. & Sodal, Sigbjorn, 2005. "Smooth pasting as rate of return equalization," Economics Letters, Elsevier, vol. 89(2), pages 200-206, November.
    8. Bunch, David S & Johnson, Herb, 1992. "A Simple and Numerically Efficient Valuation Method for American Puts Using a Modified Geske-Johnson Approach," Journal of Finance, American Finance Association, vol. 47(2), pages 809-816, June.
    9. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    10. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    11. David S. Bunch & Herb Johnson, 2000. "The American Put Option and Its Critical Stock Price," Journal of Finance, American Finance Association, vol. 55(5), pages 2333-2356, October.
    12. Broadie, Mark & Detemple, Jerome, 1996. "American Option Valuation: New Bounds, Approximations, and a Comparison of Existing Methods," Review of Financial Studies, Society for Financial Studies, vol. 9(4), pages 1211-1250.
    13. Andrew W. Stark, 2000. "Real Options, (Dis)Investment Decision-Making and Accounting Measures of Performance," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 27(3-4), pages 313-331.
    14. Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 145-166.
    15. Andrew W. Stark, 2000. "Real Options, (Dis)Investment Decision-Making and Accounting Measures of Performance," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 27(3&4), pages 313-331.
    16. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
    17. Ju, Nengjiu, 1998. "Pricing an American Option by Approximating Its Early Exercise Boundary as a Multipiece Exponential Function," Review of Financial Studies, Society for Financial Studies, vol. 11(3), pages 627-646.
    18. Geske, Robert & Johnson, Herb E, 1984. "The American Put Option Valued Analytically," Journal of Finance, American Finance Association, vol. 39(5), pages 1511-1524, December.
    19. Courtadon, Georges, 1982. "A More Accurate Finite Difference Approximation for the Valuation of Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 17(5), pages 697-703, December.
    20. Sydney D. Howell & Axel J. Jägle, 1997. "Laboratory Evidence on How Managers Intuitively Value Real Growth Options," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 24(7‐8), pages 915-935, September.
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