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Order Estimates for the Exact Lugannani-Rice Expansion

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  • Takashi Kato
  • Jun Sekine
  • Kenichi Yoshikawa
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    Abstract

    The Lugannani-Rice formula is a saddlepoint approximation method for estimating the tail probability distribution function, which was originally studied for the sum of independent identically distributed random variables. Because of its tractability, the formula is now widely used in practical financial engineering as an approximation formula for the distribution of a (single) random variable. In this paper, the Lugannani-Rice approximation formula is derived for a general, parametrized sequence of random variables and the order estimates of the approximation are given.

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    File URL: http://arxiv.org/pdf/1310.3347
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1310.3347.

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    Date of creation: Oct 2013
    Date of revision: Jun 2014
    Handle: RePEc:arx:papers:1310.3347

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    1. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-43.
    2. del Baño Rollin, Sebastian & Ferreiro-Castilla, Albert & Utzet, Frederic, 2010. "On the density of log-spot in the Heston volatility model," Stochastic Processes and their Applications, Elsevier, Elsevier, vol. 120(10), pages 2037-2063, September.
    3. C. Gourieroux, 2006. "Continuous Time Wishart Process for Stochastic Risk," Econometric Reviews, Taylor & Francis Journals, Taylor & Francis Journals, vol. 25(2-3), pages 177-217.
    4. Xiong, Jian & Wong, Augustine & Salopek, Donna, 2005. "Saddlepoint approximations to option price in a general equilibrium model," Statistics & Probability Letters, Elsevier, Elsevier, vol. 71(4), pages 361-369, March.
    5. Ai[dieresis]t-Sahalia, Yacine & Yu, Jialin, 2006. "Saddlepoint approximations for continuous-time Markov processes," Journal of Econometrics, Elsevier, Elsevier, vol. 134(2), pages 507-551, October.
    6. JosE Da Fonseca & Martino Grasselli & Claudio Tebaldi, 2008. "A multifactor volatility Heston model," Quantitative Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 8(6), pages 591-604.
    7. Joan Jasiak & R. Sufana & C. Gourieroux, 2005. "The Wishart Autoregressive Process of Multivariate Stochastic Volatility," Working Papers, York University, Department of Economics 2005_2, York University, Department of Economics.
    8. José Fonseca & Martino Grasselli & Claudio Tebaldi, 2007. "Option pricing when correlations are stochastic: an analytical framework," Review of Derivatives Research, Springer, Springer, vol. 10(2), pages 151-180, May.
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