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Numerical Inversion of Laplace Transforms: A Survey of Techniques with Applications to Derivative Pricing

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Abstract

We consider different approaches to the problem of numerically inverting Laplace transforms in finance. In particular, we discuss numerical inversion techniques in the context of Asian option pricing.

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  • Mark Craddock & David Heath & Eckhard Platen, 1999. "Numerical Inversion of Laplace Transforms: A Survey of Techniques with Applications to Derivative Pricing," Research Paper Series 27, Quantitative Finance Research Centre, University of Technology, Sydney.
  • Handle: RePEc:uts:rpaper:27
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    1. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters,in: Theory Of Valuation, chapter 5, pages 129-164 World Scientific Publishing Co. Pte. Ltd..
    2. Yoosef Maghsoodi, 1996. "Solution Of The Extended Cir Term Structure And Bond Option Valuation," Mathematical Finance, Wiley Blackwell, vol. 6(1), pages 89-109.
    3. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-592.
    4. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters,in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305 World Scientific Publishing Co. Pte. Ltd..
    5. Jamshidian, Farshid, 1989. " An Exact Bond Option Formula," Journal of Finance, American Finance Association, vol. 44(1), pages 205-209, March.
    6. 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.
    7. Schloegl, Erik & Lutz Schloegl, 1997. "A Tractable Term Structure Model with Endogenous Interpolation and Positive Interest Rates," Discussion Paper Serie B 396, University of Bonn, Germany.
    8. F. Jamshidian, 1995. "A simple class of square-root interest-rate models," Applied Mathematical Finance, Taylor & Francis Journals, vol. 2(1), pages 61-72.
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    Cited by:

    1. Xiaolin Luo & Pavel V. Shevchenko, 2009. "Computing Tails of Compound Distributions Using Direct Numerical Integration," Papers 0904.0830, arXiv.org, revised Feb 2010.
    2. Hardy Hulley & Eckhard Platen, 2007. "Laplace Transform Identities for Diffusions, with Applications to Rebates and Barrier Options," Research Paper Series 203, Quantitative Finance Research Centre, University of Technology, Sydney.
    3. Mark Craddock & Eckhard Platen, 2003. "Symmetry Group Methods for Fundamental Solutions and Characteristic Functions," Research Paper Series 90, Quantitative Finance Research Centre, University of Technology, Sydney.
    4. C. Atkinson & S. Kazantzaki, 2009. "Double knock-out Asian barrier options which widen or contract as they approach maturity," Quantitative Finance, Taylor & Francis Journals, vol. 9(3), pages 329-340.
    5. repec:hal:journl:halshs-00384398 is not listed on IDEAS
    6. Dominique Guegan & Bertrand Hassani, 2009. "A new algorithm for the loss distribution function with applications to Operational Risk Management," Documents de travail du Centre d'Economie de la Sorbonne 09023, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Nov 2009.
    7. Pavel V. Shevchenko, 2010. "Calculation of aggregate loss distributions," Papers 1008.1108, arXiv.org.
    8. repec:hal:journl:halshs-00443846 is not listed on IDEAS
    9. Xiaolin Luo & Pavel V. Shevchenko & John B. Donnelly, 2009. "Addressing the Impact of Data Truncation and Parameter Uncertainty on Operational Risk Estimates," Papers 0904.2910, arXiv.org.
    10. Nicola Bruti-Liberati & Eckhard Platen, 2007. "Approximation of jump diffusions in finance and economics," Computational Economics, Springer;Society for Computational Economics, vol. 29(3), pages 283-312, May.
    11. Dominique Guegan & Bertrand Hassani, 2009. "A modified Panjer algorithm for operational risk capital calculations," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00443846, HAL.
    12. Hardy Hulley, 2009. "Strict Local Martingales in Continuous Financial Market Models," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 19.
    13. Kwai Sun Leung & Yue Kuen Kwok, 2008. "Employee stock option valuation with repricing features," Quantitative Finance, Taylor & Francis Journals, vol. 8(6), pages 561-569.
    14. Cruz Báez, Domingo Israel & González Rodríguez, José Manuel, 2008. "Valoración de opciones. Un enfoque diferente," Estudios de Economía Aplicada, Estudios de Economía Aplicada, vol. 26, pages 341-362, Abril.

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