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Pricing Barrier Options with Time–Dependent Coefficients

Author

Listed:
  • G. O. Roberts
  • C. F. Shortland

Abstract

We consider the problem of pricing derivative securities which involve a barrier clause. We give general techniques to calculate, or estimate accurately, barrier option prices, using methods for estimating diffusion process boundary hitting times. The solution gives a simple, easy–to–use, method for calculating barrier option prices.

Suggested Citation

  • G. O. Roberts & C. F. Shortland, 1997. "Pricing Barrier Options with Time–Dependent Coefficients," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 83-93, January.
    • Handle: RePEc:bla:mathfi:v:7:y:1997:i:1:p:83-93
    DOI: 10.1111/1467-9965.00024
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    Citations

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    Cited by:

    1. Taiga Saito, 2016. "Pricing Foreign Exchange Options Under Intervention by Absorption Modeling," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 23(1), pages 85-106, March.
    2. C. Atkinson & S. Kazantzaki, 2009. "Double knock-out Asian barrier options which widen or contract as they approach maturity," Quantitative Finance, Taylor & Francis Journals, vol. 9(3), pages 329-340.
    3. repec:dau:papers:123456789/5374 is not listed on IDEAS
    4. Marco Avellaneda & Robert Buff, 1999. "Combinatorial implications of nonlinear uncertain volatility models: the case of barrier options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 6(1), pages 1-18.
    5. Bekiros, Stelios & Kouloumpou, Dimitra, 2019. "On the pricing of exotic options: A new closed-form valuation approach," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 153-162.
    6. Pötzelberger Klaus, 2012. "Improving the Monte Carlo estimation of boundary crossing probabilities by control variables," Monte Carlo Methods and Applications, De Gruyter, vol. 18(4), pages 353-377, December.
    7. Lian, Guanghua & Zhu, Song-Ping & Elliott, Robert J. & Cui, Zhenyu, 2017. "Semi-analytical valuation for discrete barrier options under time-dependent Lévy processes," Journal of Banking & Finance, Elsevier, vol. 75(C), pages 167-183.
    8. Palmowski, Zbigniew & Pistorius, Martijn, 2009. "Cramér asymptotics for finite time first passage probabilities of general Lévy processes," Statistics & Probability Letters, Elsevier, vol. 79(16), pages 1752-1758, August.
    9. Gregor Dorfleitner & Paul Schneider & Kurt Hawlitschek & Arne Buch, 2008. "Pricing options with Green's functions when volatility, interest rate and barriers depend on time," Quantitative Finance, Taylor & Francis Journals, vol. 8(2), pages 119-133.
    10. Rolf Poulsen, 2006. "Barrier options and their static hedges: simple derivations and extensions," Quantitative Finance, Taylor & Francis Journals, vol. 6(4), pages 327-335.
    11. K. Borovkov & Alexander Novikov, 2004. "Explicit Bounds for Approximation Rates for Boundary Crossing Probabilities for the Wiener Process," Research Paper Series 115, Quantitative Finance Research Centre, University of Technology, Sydney.
    12. Nina Kordzakhia & Alex Novikov, 2007. "Pricing of Defaultable Securities Under Stochastic Interest," Research Paper Series 193, Quantitative Finance Research Centre, University of Technology, Sydney.
    13. Zhang, Xiaoyuan & Zhang, Tianqi, 2022. "Barrier option pricing under a Markov Regime switching diffusion model," The Quarterly Review of Economics and Finance, Elsevier, vol. 86(C), pages 273-280.

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