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Double Lookbacks

Author

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  • Hua He William P. Keirstead and Joachim Rebholz.

Abstract

A new class of options, double lookbacks, where the payoffs depend on the maximum and/or minimum prices of one or two traded assets is introduced and analyzed. This class of double lookbacks includes calls and puts with the underlying being the difference between the maximum and minimum prices of one asset over a certain period, and calls or puts with the underlying being the difference between the maximum prices of two correlated assets over a certain period. Analytical expressions of the joint probability distribution of the maximum and minimum values of two correlated geometric Brownian motions are derived and used in the valuation of double lookbacks. Numerical results are shown, and prices of double lookbacks are compared to those of standard lookbacks on a single asset.

Suggested Citation

  • Hua He William P. Keirstead and Joachim Rebholz., 1995. "Double Lookbacks," Research Program in Finance Working Papers RPF-248, University of California at Berkeley.
    • Handle: RePEc:ucb:calbrf:rpf-248
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    Cited by:

    1. Prigent, Jean-Luc & Renault, Olivier & Scaillet, Olivier, 2004. "Option pricing with discrete rebalancing," Journal of Empirical Finance, Elsevier, vol. 11(1), pages 133-161, January.
    2. Alexander Lipton & Andrey Gal & Andris Lasis, 2014. "Pricing of vanilla and first-generation exotic options in the local stochastic volatility framework: survey and new results," Quantitative Finance, Taylor & Francis Journals, vol. 14(11), pages 1899-1922, November.
    3. de Paula, Áureo, 2009. "Inference in a synchronization game with social interactions," Journal of Econometrics, Elsevier, vol. 148(1), pages 56-71, January.
    4. Farid MKAOUAR & Jean-luc PRIGENT, 2014. "Constant Proportion Portfolio Insurance under Tolerance and Transaction Costs," Working Papers 2014-303, Department of Research, Ipag Business School.
    5. Takahiko Fujita & Masahiro Ishii, 2010. "Valuation of a Repriceable Executive Stock Option," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 17(1), pages 1-18, March.
    6. Abínzano, Isabel & Seco, Luis & Escobar, Marcos & Olivares, Pablo, 2009. "Single and Double Black-Cox: Two approaches for modelling debt restructuring," Economic Modelling, Elsevier, vol. 26(5), pages 910-917, September.
    7. Marcos Escobar & Peter Hieber & Matthias Scherer, 2014. "Efficiently pricing double barrier derivatives in stochastic volatility models," Review of Derivatives Research, Springer, vol. 17(2), pages 191-216, July.
    8. Pavel V. Shevchenko & Pierre Del Moral, 2014. "Valuation of Barrier Options using Sequential Monte Carlo," Papers 1405.5294, arXiv.org, revised Jul 2015.
    9. Lie-Jane Kao, 2016. "Credit valuation adjustment of cap and floor with counterparty risk: a structural pricing model for vulnerable European options," Review of Derivatives Research, Springer, vol. 19(1), pages 41-64, April.
    10. Tristan Guillaume, 2011. "Some sequential boundary crossing results for geometric Brownian motion and their applications in financial engineering," Post-Print hal-00924277, HAL.
    11. Alexander Lipton & Ioana Savescu, 2012. "A structural approach to pricing credit default swaps with credit and debt value adjustments," Papers 1206.3104, arXiv.org.
    12. 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.
    13. Alexander Lipton & Ioana Savescu, 2012. "Pricing credit default swaps with bilateral value adjustments," Papers 1207.6049, arXiv.org.
    14. Patras, Frédéric, 2006. "A reflection principle for correlated defaults," Stochastic Processes and their Applications, Elsevier, vol. 116(4), pages 690-698, April.
    15. Vadim Kaushansky & Alexander Lipton & Christoph Reisinger, 2017. "Transition probability of Brownian motion in the octant and its application to default modeling," Papers 1801.00362, arXiv.org, revised May 2018.

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