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Quanto Lookback Options

Author

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  • Min Dai
  • Hoi Ying Wong
  • Yue Kuen Kwok

Abstract

The lookback feature in a quanto option refers to the payoff structure where the terminal payoff of the quanto option depends on the realized extreme value of either the stock price or the exchange rate. In this paper, we study the pricing models of European and American lookback options with the quanto feature. The analytic price formulas for two types of European‐style quanto lookback options are derived. The success of the analytic tractability of these quanto lookback options depends on the availability of a succinct analytic representation of the joint density function of the extreme value and terminal value of the stock price and exchange rate. We also analyze the early exercise policies and pricing behaviors of the quanto lookback options with the American feature. The early exercise boundaries of these American quanto lookback options exhibit properties that are distinctive from other two‐state American option models.

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  • Min Dai & Hoi Ying Wong & Yue Kuen Kwok, 2004. "Quanto Lookback Options," Mathematical Finance, Wiley Blackwell, vol. 14(3), pages 445-467, July.
    • Handle: RePEc:bla:mathfi:v:14:y:2004:i:3:p:445-467
    DOI: 10.1111/j.0960-1627.2004.00199.x
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    Cited by:

    1. Ha, Mijin & Kim, Donghyun & Yoon, Ji-Hun, 2024. "Valuing of timer path-dependent options," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 215(C), pages 208-227.
    2. Sun-Yong Choi & Ji-Hun Yoon & Junkee Jeon, 2019. "Pricing of Fixed-Strike Lookback Options on Assets with Default Risk," Mathematical Problems in Engineering, Hindawi, vol. 2019, pages 1-10, January.
    3. Lee, Hangsuck & Ha, Hongjun & Kim, Eunchae & Lee, Minha, 2024. "Quanto fund protection using partial lookback participation," The North American Journal of Economics and Finance, Elsevier, vol. 73(C).
    4. Kim, Geonwoo & Jeon, Junkee, 2018. "Closed-form solutions for valuing partial lookback options with random initiation," Finance Research Letters, Elsevier, vol. 24(C), pages 321-327.
    5. Wong, Hoi Ying & Chan, Chun Man, 2007. "Lookback options and dynamic fund protection under multiscale stochastic volatility," Insurance: Mathematics and Economics, Elsevier, vol. 40(3), pages 357-385, May.
    6. Tianyao Chen & Xue Cheng & Jingping Yang, 2019. "Common Decomposition of Correlated Brownian Motions and its Financial Applications," Papers 1907.03295, arXiv.org, revised Nov 2020.
    7. Lee, Hangsuck & Ha, Hongjun & Lee, Minha, 2023. "Partial quanto lookback options," The North American Journal of Economics and Finance, Elsevier, vol. 64(C).
    8. Li, Zhe & Zhang, Wei-Guo & Liu, Yong-Jun, 2018. "European quanto option pricing in presence of liquidity risk," The North American Journal of Economics and Finance, Elsevier, vol. 45(C), pages 230-244.
    9. Lee, Hangsuck & Ha, Hongjun & Lee, Minha, 2022. "Foreign equity lookback options with guarantees," Finance Research Letters, Elsevier, vol. 48(C).

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