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Pricing Barrier Options With Square Root Process

Author

Listed:
  • C. F. LO

    (Department of Physics, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong, China)

  • P. H. YUEN

    (Department of Physics, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong, China)

  • C. H. HUI

    (Banking Policy Department, Hong Kong Monetary Authority, Hong Kong, China)

Abstract

The square root constant elasticity of variance (CEV) process has been paid little attention in previous research on valuation of barrier options. In this paper we derive analytical option pricing formulae of up-and-out options with this process using the eigenfunction expansion technique. We develop an efficient algorithm to compute the eigenvalues where the basis functions in the formulae are the confluent hypergeometric functions. The numerical results obtained from the formulae are compared with the corresponding model prices under the Black–Scholes model. We find that the differences in the model prices between the square root CEV model and the Black–Scholes model can be significant as the time to maturity and volatility increases.

Suggested Citation

  • C. F. Lo & P. H. Yuen & C. H. Hui, 2001. "Pricing Barrier Options With Square Root Process," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 4(05), pages 805-818.
    • Handle: RePEc:wsi:ijtafx:v:04:y:2001:i:05:n:s021902490100122x
    DOI: 10.1142/S021902490100122X
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    Citations

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    Cited by:

    1. Shane Miller, 2007. "Pricing of Contingent Claims Under the Real-World Measure," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 2-2007, January-A.
    2. Campi, L. & Polbennikov, S.Y. & Sbuelz, A., 2005. "Assessing Credit with Equity : A CEV Model with Jump to Default," Other publications TiSEM 21b78fcf-8401-4e4d-8224-7, Tilburg University, School of Economics and Management.
    3. Angelos Dassios & Jayalaxshmi Nagaradjasarma, 2006. "The square-root process and Asian options," Quantitative Finance, Taylor & Francis Journals, vol. 6(4), pages 337-347.
    4. Campi, L. & Polbennikov, S.Y. & Sbuelz, A., 2005. "Assessing Credit with Equity : A CEV Model with Jump to Default," Discussion Paper 2005-27, Tilburg University, Center for Economic Research.
    5. Campi, L. & Sbuelz, A., 2005. "Close-Form Pricing of Benchmark Equity Default Swaps Under the CEV Assumption," Discussion Paper 2005-28, Tilburg University, Center for Economic Research.
    6. Dassios, Angelos & Nagaradjasarma, Jayalaxshmi, 2006. "The square-root process and Asian options," LSE Research Online Documents on Economics 2851, London School of Economics and Political Science, LSE Library.
    7. Luciano Campi & Simon Polbennikov & Sbuelz, 2005. "Assessing Credit with Equity: A CEV Model with Jump to Default," Working Papers 24/2005, University of Verona, Department of Economics.
    8. Fusai, Gianluca & Recchioni, Maria Cristina, 2007. "Analysis of quadrature methods for pricing discrete barrier options," Journal of Economic Dynamics and Control, Elsevier, vol. 31(3), pages 826-860, March.
    9. Campi, Luciano & Polbennikov, Simon & Sbuelz, Alessandro, 2009. "Systematic equity-based credit risk: A CEV model with jump to default," Journal of Economic Dynamics and Control, Elsevier, vol. 33(1), pages 93-108, January.
    10. Campi, L. & Sbuelz, A., 2005. "Close-Form Pricing of Benchmark Equity Default Swaps Under the CEV Assumption," Other publications TiSEM f10edfa3-d4c3-489b-bffe-4, Tilburg University, School of Economics and Management.

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