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Pricing of the European Options by Spectral Theory

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  • Dell'Era Mario, M.D.
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    Abstract

    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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    Bibliographic Info

    Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 17429.

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    Date of creation: 25 Mar 2008
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    Handle: RePEc:pra:mprapa:17429

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    Keywords: Options Pricing; Computation Complexity.;

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    1. Dmitry Davydov & Vadim Linetsky, 2001. "Pricing and Hedging Path-Dependent Options Under the CEV Process," Management Science, INFORMS, INFORMS, vol. 47(7), pages 949-965, July.
    2. 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.
    3. Peter Carr & Katrina Ellis & Vishal Gupta, 1998. "Static Hedging of Exotic Options," Journal of Finance, American Finance Association, vol. 53(3), pages 1165-1190, 06.
    4. 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.
    5. Antoon Pelsser, . "Pricing Double Barrier Options: An Analytical Approach," Computing in Economics and Finance 1997 130, Society for Computational Economics.
    6. Mark Broadie & Paul Glasserman & Steven Kou, 1997. "A Continuity Correction for Discrete Barrier Options," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 7(4), pages 325-349.
    7. Christoph Gallus, 1999. "Exploding hedging errors for digital options," Finance and Stochastics, Springer, vol. 3(2), pages 187-201.
    8. 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.
    9. Fitzsimmons, P. J. & Pitman, Jim, 1999. "Kac's moment formula and the Feynman-Kac formula for additive functionals of a Markov process," Stochastic Processes and their Applications, Elsevier, vol. 79(1), pages 117-134, January.
    10. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
    11. 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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