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From Characteristic Function to Distribution Function: A Simple Framework for the Theory

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  • Shephard, N.G.

Abstract

A unified framework is established for the study of the computation of the distribution function from the characteristic function. A new approach to the proof of Gurland's and Gil-Pelaez's univariate inversion theorem is suggested. A multivariate inversion theorem is then derived using this technique.

Suggested Citation

  • Shephard, N.G., 1991. "From Characteristic Function to Distribution Function: A Simple Framework for the Theory," Econometric Theory, Cambridge University Press, vol. 7(04), pages 519-529, December.
  • Handle: RePEc:cup:etheor:v:7:y:1991:i:04:p:519-529_00
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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. Simon A. Broda & Raymond Kan, 2016. "On distributions of ratios," Biometrika, Biometrika Trust, vol. 103(1), pages 205-218.
    3. Simon Trimborn & Wolfgang Karl Härdle, 2015. "CRIX or evaluating Blockchain based currencies," SFB 649 Discussion Papers SFB649DP2015-048, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    4. Oleksandr Zhylyevskyy, 2010. "A fast Fourier transform technique for pricing American options under stochastic volatility," Review of Derivatives Research, Springer, vol. 13(1), pages 1-24, April.
    5. Simi, Wei W. & Wang, Xiaoli, 2013. "Time-changed Lévy jump processes with GARCH model on reverse convertibles," Review of Financial Economics, Elsevier, vol. 22(4), pages 206-212.
    6. repec:eee:apmaco:v:273:y:2016:i:c:p:741-758 is not listed on IDEAS
    7. Carl Chiarella & Jonathan Ziveyi, 2011. "Two Stochastic Volatility Processes - American Option Pricing," Research Paper Series 292, Quantitative Finance Research Centre, University of Technology, Sydney.
    8. Jonathan Ziveyi, 2011. "The Evaluation of Early Exercise Exotic Options," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 12.
    9. Zhylyevskyy, Oleksandr, 2012. "Joint Characteristic Function of Stock Log-Price and Squared Volatility in the Bates Model and Its Asset Pricing Applications," Staff General Research Papers Archive 35559, Iowa State University, Department of Economics.
    10. Susanne Griebsch & Uwe Wystup, 2011. "On the valuation of fader and discrete barrier options in Heston's stochastic volatility model," Quantitative Finance, Taylor & Francis Journals, vol. 11(5), pages 693-709.
    11. Bakshi, Gurdip & Madan, Dilip, 2000. "Spanning and derivative-security valuation," Journal of Financial Economics, Elsevier, vol. 55(2), pages 205-238, February.
    12. Pavel V. Shevchenko, 2010. "Calculation of aggregate loss distributions," Papers 1008.1108, arXiv.org.

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