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Closed-form solutions for valuing partial lookback options with random initiation

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  • Kim, Geonwoo
  • Jeon, Junkee

Abstract

In this paper, we propose new types of partial lookback options, where the underlying asset price has to cross a predetermined barrier to activate the standard lookback option. Reflection principle and Girsanov theorem are used to derive the closed-form pricing formulas for the partial lookback options with random initiation. We also verify our pricing formulas by comparing it with the Monte Carlo simulation results and provide the experiment results with graphs to illustrate the properties of the proposed options with respect to parameters.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:finlet:v:24:y:2018:i:c:p:321-327
    DOI: 10.1016/j.frl.2017.09.019
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    References listed on IDEAS

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    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. Peter Buchen & Otto Konstandatos, 2005. "A New Method Of Pricing Lookback Options," Mathematical Finance, Wiley Blackwell, vol. 15(2), pages 245-259, April.
    3. Farid Aitsahlia & Tzeung Le Lai, 1998. "Random walk duality and the valuation of discrete lookback options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 5(3-4), pages 227-240.
    4. Min Dai & Hoi Ying Wong & Yue Kuen Kwok, 2004. "Quanto Lookback Options," Mathematical Finance, Wiley Blackwell, vol. 14(3), pages 445-467, July.
    5. Han, Heejae & Jeon, Junkee & Kang, Myungjoo, 2016. "Pricing chained dynamic fund protection," The North American Journal of Economics and Finance, Elsevier, vol. 37(C), pages 267-278.
    6. Hans-Peter Bermin, 2000. "Hedging lookback and partial lookback options using Malliavin calculus," Applied Mathematical Finance, Taylor & Francis Journals, vol. 7(2), pages 75-100.
    7. 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.
    8. R. C. Heynen & H. M. Kat, 1995. "Lookback options with discrete and partial monitoring of the underlying price," Applied Mathematical Finance, Taylor & Francis Journals, vol. 2(4), pages 273-284.
    9. Hans-Peter Bermin & Peter Buchen & Otto Konstandatos, 2008. "Two Exotic Lookback Options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 15(4), pages 387-402.
    10. Boyle, Phelim P. & Tian, Yisong “Sam”, 1999. "Pricing Lookback and Barrier Options under the CEV Process," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(2), pages 241-264, June.
    11. Hoi Ying Wong & Chun Man Chan, 2008. "Turbo warrants under stochastic volatility," Quantitative Finance, Taylor & Francis Journals, vol. 8(7), pages 739-751.
    12. Park, Sang-Hyeon & Kim, Jeong-Hoon, 2013. "A semi-analytic pricing formula for lookback options under a general stochastic volatility model," Statistics & Probability Letters, Elsevier, vol. 83(11), pages 2537-2543.
    13. Liming Feng & Vadim Linetsky, 2009. "Computing exponential moments of the discrete maximum of a Lévy process and lookback options," Finance and Stochastics, Springer, vol. 13(4), pages 501-529, September.
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    Cited by:

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    2. Deng, Guohe, 2020. "Pricing perpetual American floating strike lookback option under multiscale stochastic volatility model," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).

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