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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.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 17502.

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Date of creation: 25 Mar 2008
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Handle: RePEc:pra:mprapa:17502

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Related research

Keywords: Options Pricing; Computation Complexity.;

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References

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  1. 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.
  2. Antoon Pelsser, . "Pricing Double Barrier Options: An Analytical Approach," Computing in Economics and Finance 1997 130, Society for Computational Economics.
  3. 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.
  4. Mark Broadie & Paul Glasserman & Steven Kou, 1997. "A Continuity Correction for Discrete Barrier Options," Mathematical Finance, Wiley Blackwell, vol. 7(4), pages 325-349.
  5. Dmitry Davydov & Vadim Linetsky, 2001. "Pricing and Hedging Path-Dependent Options Under the CEV Process," Management Science, INFORMS, vol. 47(7), pages 949-965, July.
  6. 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.
  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. 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.
  10. 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 637-54, May-June.
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