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Pricing formula of Lookback option in stochastic delay differential equation model

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  • Il-Kwang, Paek
  • Chol-Su, Kang
  • Kyong-Hui, Kim

Abstract

This paper deals with new explicit pricing formulae for Lookback option when underlying asset price processes are represented by stochastic delay differential equation (hereafter “SDDE”). We derive a lemma on the joint distribution of the minimum and itself of a Wiener process in the SDDE model. Using this lemma, we obtain the explicit pricing formulae for the Lookback option. Through some numerical comparison experiment, we assure the correctness of the obtained pricing formula.

Suggested Citation

  • Il-Kwang, Paek & Chol-Su, Kang & Kyong-Hui, Kim, 2025. "Pricing formula of Lookback option in stochastic delay differential equation model," Statistics & Probability Letters, Elsevier, vol. 216(C).
    • Handle: RePEc:eee:stapro:v:216:y:2025:i:c:s0167715224002529
    DOI: 10.1016/j.spl.2024.110283
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    References listed on IDEAS

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    1. Jin‐Chuan Duan, 1995. "The Garch Option Pricing Model," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 13-32, January.
    2. Kazmerchuk, Yuriy & Swishchuk, Anatoliy & Wu, Jianhong, 2007. "The pricing of options for securities markets with delayed response," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 75(3), pages 69-79.
    3. Margrabe, William, 1978. "The Value of an Option to Exchange One Asset for Another," Journal of Finance, American Finance Association, vol. 33(1), pages 177-186, March.
    4. Hull, John C & White, Alan D, 1987. "The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
    5. repec:dau:papers:123456789/5374 is not listed on IDEAS
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