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Two extensions to barrier option valuation

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  • P. Carr

Abstract

We first present a brief but essentially complete survey of the literature on barrier option pricing. We then present two extensions of European up-and-out call option valuation. The first allows for an initial protection period during which the option cannot be knocked out. The second considers an option which is only knocked out if a second asset touches an upper barrier. Closed form solutions, detailed derivations, and the economic rationale for both types of options are provided.

Suggested Citation

  • P. Carr, 1995. "Two extensions to barrier option valuation," Applied Mathematical Finance, Taylor & Francis Journals, vol. 2(3), pages 173-209.
  • Handle: RePEc:taf:apmtfi:v:2:y:1995:i:3:p:173-209 DOI: 10.1080/13504869500000010
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    Cited by:

    1. Kim, Jerim & Kim, Jeongsim & Joo Yoo, Hyun & Kim, Bara, 2015. "Pricing external barrier options in a regime-switching model," Journal of Economic Dynamics and Control, Elsevier, vol. 53(C), pages 123-143.
    2. Andrew Ming-Long Wang & Yu-Hong Liu & Yi-Long Hsiao, 2009. "Barrier option pricing: a hybrid method approach," Quantitative Finance, Taylor & Francis Journals, pages 341-352.
    3. Julien Azzaz & Stéphane Loisel & Pierre-E. Thérond, 2015. "Some characteristics of an equity security next-year impairment," Review of Quantitative Finance and Accounting, Springer, pages 111-135.
    4. Norland, Erik & Wilford, D. Sykes, 2002. "Leverage, liquidity, volatility, time horizon, and the risk of ruin: A barrier option approach," Review of Financial Economics, Elsevier, vol. 11(3), pages 225-239.
    5. Tristan Guillaume, 2001. "valuation of options on joint minima and maxima," Applied Mathematical Finance, Taylor & Francis Journals, pages 209-233.
    6. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742.
    7. Grant Armstrong, 2001. "Valuation formulae for window barrier options," Applied Mathematical Finance, Taylor & Francis Journals, pages 197-208.
    8. Ravi Kashyap, 2016. "Securities Lending Strategies, Valuation of Term Loans using Option Theory," Papers 1609.01274, arXiv.org, revised Nov 2016.
    9. Jokivuolle, Esa & Keppo, Jussi, 2014. "Bankers' compensation: : Sprint swimming in short bonus pools?," Research Discussion Papers 2/2014, Bank of Finland.
    10. Jan Ericsson & Joel Reneby, 2003. "Stock options as barrier contingent claims," Applied Mathematical Finance, Taylor & Francis Journals, pages 121-147.
    11. Ballestra, Luca Vincenzo & Pacelli, Graziella & Zirilli, Francesco, 2007. "A numerical method to price exotic path-dependent options on an underlying described by the Heston stochastic volatility model," Journal of Banking & Finance, Elsevier, vol. 31(11), pages 3420-3437, November.
    12. Zvan, R. & Vetzal, K. R. & Forsyth, P. A., 2000. "PDE methods for pricing barrier options," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1563-1590, October.
    13. Dietmar P.J. Leisen, 1999. "Valuation of Barrier Options in a Black--Scholes Setup with Jump Risk," Discussion Paper Serie B 446, University of Bonn, Germany.
    14. repec:hal:wpaper:hal-00820929 is not listed on IDEAS
    15. Jan Ericsson & Joel Reneby, 2003. "Stock options as barrier contingent claims," Applied Mathematical Finance, Taylor & Francis Journals, pages 121-147.
    16. Hans-Peter Bermin, 2000. "Hedging lookback and partial lookback options using Malliavin calculus," Applied Mathematical Finance, Taylor & Francis Journals, pages 75-100.
    17. Feng, Yun & Huang, Bing-hua & Young, Martin & Zhou, Qi-yuan, 2015. "Decomposing and valuing convertible bonds: A new method based on exotic options," Economic Modelling, Elsevier, vol. 47(C), pages 193-206.

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    Keywords

    option pricing; exotic options;

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