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Valuing American Fractional Lookback Options

Author

Listed:
  • Hangsuck Lee
  • Yisub Kye
  • Haewon Seo
  • Donghyun Kim
  • Hongjun Ha

Abstract

This study presents an analytical framework for the valuation of American fractional floating‐strike lookback options, taking into account both path dependency and the possibility of early exercise. The proposed pricing methodology is based on the Mellin transform technique, through which we derive and solve the associated partial differential equations governing the pricing functions. A key contribution of this work is the explicit characterization of the early‐exercise premium via an integral equation, in contrast to existing methods that typically rely on implicit expressions obtained through inverse transformations. This explicit form provides a more transparent understanding of the structure and behavior of the early‐exercise premium. Numerical experiments are conducted to confirm the accuracy and stability of the proposed approach in approximating the true option values.

Suggested Citation

  • Hangsuck Lee & Yisub Kye & Haewon Seo & Donghyun Kim & Hongjun Ha, 2026. "Valuing American Fractional Lookback Options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 46(9), pages 1475-1500, September.
    • Handle: RePEc:wly:jfutmk:v:46:y:2026:i:9:p:1475-1500
    DOI: 10.1002/fut.70115
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    References listed on IDEAS

    as
    1. Gerber, Hans U. & Shiu, Elias S. W., 1996. "Actuarial bridges to dynamic hedging and option pricing," Insurance: Mathematics and Economics, Elsevier, vol. 18(3), pages 183-218, November.
    2. Conze, Antoine & Viswanathan, 1991. "Path Dependent Options: The Case of Lookback Options," Journal of Finance, American Finance Association, vol. 46(5), pages 1893-1907, December.
    3. Donghyun Kim & Ji-Hun Yoon, 2023. "Analytic Method for Pricing Vulnerable External Barrier Options," Computational Economics, Springer;Society for Computational Economics, vol. 61(4), pages 1561-1591, April.
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