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Pricing of Double Barrier Options by Spectral Theory

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  • Dell'Era Mario, M.D.

Abstract

We propose to discuss the efficiency of the spectral method for computing the value of Double Barrier Options. Using this method, one may write the option price as a Fourier series, with suitable coefficients. We propose a simple approach for its computing. One consider the general case, in which the volatility is time dependent, but it is immediate extend our methodology also in the case of constant volatility. The advantage to write the arbitrage price of the Double Barrier Options as Fourier series, is matter of computation complexity. The methods used to evaluate options of this kind have a high value of computation complexity, furthermore, them have not the capacity to manage it, while using our method, one can define, through an easy analytical report, the computation complexity of the problem, and also one can choice its accuracy.

Suggested Citation

  • Dell'Era Mario, M.D., 2008. "Pricing of Double Barrier Options by Spectral Theory," MPRA Paper 17502, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:17502
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    File URL: https://mpra.ub.uni-muenchen.de/17548/2/MPRA_paper_17548.pdf
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    References listed on IDEAS

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    2. Antoon Pelsser, "undated". "Pricing Double Barrier Options: An Analytical Approach," Computing in Economics and Finance 1997 130, Society for Computational Economics.
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    4. Broadie, Mark & Cvitanic, Jaksa & Soner, H Mete, 1998. "Optimal Replication of Contingent Claims under Portfolio Constraints," Review of Financial Studies, Society for Financial Studies, vol. 11(1), pages 59-79.
    5. Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 145-166.
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    8. Miura, Ryozo, 1992. "A Note on Look-Back Options Based on Order Statistics," Hitotsubashi Journal of commerce and management, Hitotsubashi University, vol. 27(1), pages 15-28, November.
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    11. Mark Broadie & Paul Glasserman & Steven Kou, 1997. "A Continuity Correction for Discrete Barrier Options," Mathematical Finance, Wiley Blackwell, vol. 7(4), pages 325-349.
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    More about this item

    Keywords

    Options Pricing; Computation Complexity.;

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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