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Sub-Replication and Replenishing Premium: Efficient Pricing of Multi-State Lookbacks


  • Hoi Wong


  • Yue Kwok



The direct valuation procedure of performing discounted expectation to obtain the prices of multi-state lookback options may lead to insurmountable complexity and numerical difficulties. The computation may require numerical differentiation of the joint distribution function of the extremum values, then followed by numerical integration over a semi-infinite domain. In this paper, we illustrate the use of an alternative approach that significantly simplifies the calculations of multi-state lookback option prices. The financial intuition behind the new approach involves the choice of a sub-replicating portfolio and the adoption of the corresponding replenishing strategy to achieve the subsequent full replication of the derivative. The replenishing premium is obtained by performing the integration of an appropriate distribution function over the range of asset price within which under replication occurs. The sub-replication and replenishment procedures may be utilized as hedging strategies for the lookback options. The pricing and hedging properties of multi-state lookback options are also discussed. Copyright Kluwer Academic Publishers 2003

Suggested Citation

  • Hoi Wong & Yue Kwok, 2003. "Sub-Replication and Replenishing Premium: Efficient Pricing of Multi-State Lookbacks," Review of Derivatives Research, Springer, vol. 6(2), pages 83-106, May.
  • Handle: RePEc:kap:revdev:v:6:y:2003:i:2:p:83-106
    DOI: 10.1023/A:1027377228682

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    References listed on IDEAS

    1. Goldman, M Barry & Sosin, Howard B & Gatto, Mary Ann, 1979. "Path Dependent Options: "Buy at the Low, Sell at the High"," Journal of Finance, American Finance Association, vol. 34(5), pages 1111-1127, December.
    2. Zhou, Chunsheng, 2001. "An Analysis of Default Correlations and Multiple Defaults," Review of Financial Studies, Society for Financial Studies, vol. 14(2), pages 555-576.
    3. 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.
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    Cited by:

    1. Leunglung Chan & Song-Ping Zhu, 2014. "An exact and explicit formula for pricing lookback options with regime switching," Papers 1407.4864,
    2. Chu, Chi Chiu & Kwok, Yue Kuen, 2004. "Reset and withdrawal rights in dynamic fund protection," Insurance: Mathematics and Economics, Elsevier, vol. 34(2), pages 273-295, April.
    3. 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.


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