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Double Lookbacks

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  • Hua He
  • William P. Keirstead
  • Joachim Rebholz
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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. Copyright Blackwell Publishers Inc 1998.

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Bibliographic Info

Article provided by Wiley Blackwell in its journal Mathematical Finance.

Volume (Year): 8 (1998)
Issue (Month): 3 ()
Pages: 201-228

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Handle: RePEc:bla:mathfi:v:8:y:1998:i:3:p:201-228

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Cited by:
  1. Jean-Luc PRIGENT & Olivier RENAULT & Olivier SCAILLET, 2002. "Option Pricing with Discrete Rebalancing," FAME Research Paper Series rp55, International Center for Financial Asset Management and Engineering.
  2. Takahiko Fujita & Masahiro Ishii, 2010. "Valuation of a Repriceable Executive Stock Option," Asia-Pacific Financial Markets, Springer, vol. 17(1), pages 1-18, March.
  3. Aureo de Paula, 2004. "Inference in a Synchronization Game with Social Interactions," PIER Working Paper Archive 07-017, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 01 May 2007.
  4. Alexander Lipton & Ioana Savescu, 2012. "A structural approach to pricing credit default swaps with credit and debt value adjustments," Papers 1206.3104, arXiv.org.
  5. Alexander Lipton & Ioana Savescu, 2012. "Pricing credit default swaps with bilateral value adjustments," Papers 1207.6049, arXiv.org.
  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. Tristan Guillaume, 2011. "Some sequential boundary crossing results for geometric Brownian motion and their applications in financial engineering," Post-Print hal-00924277, HAL.
  8. Pavel V. Shevchenko & Pierre Del Moral, 2014. "Valuation of Barrier Options using Sequential Monte Carlo," Papers 1405.5294, arXiv.org.
  9. 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.
  10. 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.
  11. Patras, Frédéric, 2006. "A reflection principle for correlated defaults," Stochastic Processes and their Applications, Elsevier, vol. 116(4), pages 690-698, April.
  12. 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.

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