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Pricing of the European Options by Spectral Theory


  • Dell'Era Mario, M.D.


We discuss the efficiency of the spectral method for computing the value of the European Call Options, which is based upon the Fourier series expansion. We propose a simple approach for computing accurate estimates. We consider the general case, in which the volatility is time dependent, but it is immediate extend our methodology at the case of constant volatility. The advantage to write the arbitrage price of the European Call Options as Fourier series, is matter of computation complexity. Infact, 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. We can define, by an easy analytical relation, the computation complexity of the problem in the framework of general theory of the ”Function Analysis”, called The Spectral Theory.

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  • Dell'Era Mario, M.D., 2008. "Pricing of the European Options by Spectral Theory," MPRA Paper 17429, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:17429

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    1. repec:wsi:ijtafx:v:02:y:1999:i:01:n:s0219024999000030 is not listed on IDEAS
    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.
    6. Raphael Douady, 1999. "Closed Form Formulas For Exotic Options And Their Lifetime Distribution," World Scientific Book Chapters,in: Quantitative Analysis In Financial Markets Collected Papers of the New York University Mathematical Finance Seminar, chapter 6, pages 177-202 World Scientific Publishing Co. Pte. Ltd..
    7. Peter Carr & Katrina Ellis & Vishal Gupta, 1998. "Static Hedging of Exotic Options," Journal of Finance, American Finance Association, vol. 53(3), pages 1165-1190, June.
    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.
    9. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    10. Boyle, Phelim P. & Tian, Yisong “Sam”, 1999. "Pricing Lookback and Barrier Options under the CEV Process," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(02), pages 241-264, June.
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    13. Christoph Gallus, 1999. "Exploding hedging errors for digital options," Finance and Stochastics, Springer, vol. 3(2), pages 187-201.
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    More about this item


    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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