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Exercise Regions And Efficient Valuation Of American Lookback Options

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  • Tze Leung Lai
  • Tiong Wee Lim

Abstract

This paper presents an efficient method to compute the values and early exercise boundaries of American fixed strike lookback options. The method reduces option valuation to a single optimal stopping problem for standard Brownian motion and an associated path‐dependent functional, indexed by one parameter in the absence of dividends and by two parameters in the presence of a dividend rate. Numerical results obtained by this method show that, after a space‐time transformation, the stopping boundaries are well approximated by certain piecewise linear functions with a few pieces, leading to fast and accurate approximations for American lookback option values. An explicit decomposition formula for American lookback options is derived and applied not only to the development of these approximations but also to the asymptotic analysis of the early exercise boundary near the expiration date.

Suggested Citation

  • Tze Leung Lai & Tiong Wee Lim, 2004. "Exercise Regions And Efficient Valuation Of American Lookback Options," Mathematical Finance, Wiley Blackwell, vol. 14(2), pages 249-269, April.
    • Handle: RePEc:bla:mathfi:v:14:y:2004:i:2:p:249-269
    DOI: 10.1111/j.0960-1627.2004.00191.x
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    Cited by:

    1. San‐Lin Chung & Yi‐Ta Huang & Pai‐Ta Shih & Jr‐Yan Wang, 2019. "Semistatic hedging and pricing American floating strike lookback options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 39(4), pages 418-434, April.
    2. Min Dai & Zuo Quan Xu, 2009. "Optimal Redeeming Strategy of Stock Loans," Papers 0906.0702, arXiv.org.
    3. L. Ramprasath, 2018. "A simpler algorithm to price American Lookback options in a discrete stochastic volatility model," Working papers 294, Indian Institute of Management Kozhikode.
    4. Zhaoqiang Yang, 2017. "Efficient valuation and exercise boundary of American fractional lookback option in a mixed jump-diffusion model," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(02n03), pages 1-29, June.
    5. Min Dai & Yue Kuen Kwok, 2006. "Characterization Of Optimal Stopping Regions Of American Asian And Lookback Options," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 63-82, January.
    6. Leonardo Kanashiro Felizardo & Elia Matsumoto & Emilio Del-Moral-Hernandez, 2022. "Solving the optimal stopping problem with reinforcement learning: an application in financial option exercise," Papers 2208.00765, arXiv.org.

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