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Asymptotic Formulas with Error Estimates for Call Pricing Functions and the Implied Volatility at Extreme Strikes

  • A. Gulisashvili
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    In this paper, we obtain asymptotic formulas with error estimates for the implied volatility associated with a European call pricing function. We show that these formulas imply Lee's moment formulas for the implied volatility and the tail-wing formulas due to Benaim and Friz. In addition, we analyze Pareto-type tails of stock price distributions in uncorrelated Hull-White, Stein-Stein, and Heston models and find asymptotic formulas with error estimates for call pricing functions in these models.

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    File URL: http://arxiv.org/pdf/0906.0394
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    Paper provided by arXiv.org in its series Papers with number 0906.0394.

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    Date of creation: Jun 2009
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    Handle: RePEc:arx:papers:0906.0394
    Contact details of provider: Web page: http://arxiv.org/

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    1. Archil Gulisashvili & Elias M. Stein, 2009. "Implied Volatility In The Hull-White Model," Mathematical Finance, Wiley Blackwell, vol. 19(2), pages 303-327.
    2. Hans Buehler, 2006. "Expensive martingales," Quantitative Finance, Taylor & Francis Journals, vol. 6(3), pages 207-218.
    3. René Carmona & Sergey Nadtochiy, 2009. "Local volatility dynamic models," Finance and Stochastics, Springer, vol. 13(1), pages 1-48, January.
    4. Eric Renault & Nizar Touzi, 1996. "Option Hedging And Implied Volatilities In A Stochastic Volatility Model," Mathematical Finance, Wiley Blackwell, vol. 6(3), pages 279-302.
    5. Carr, Peter & Madan, Dilip B., 2005. "A note on sufficient conditions for no arbitrage," Finance Research Letters, Elsevier, vol. 2(3), pages 125-130, September.
    6. Cousot, Laurent, 2007. "Conditions on option prices for absence of arbitrage and exact calibration," Journal of Banking & Finance, Elsevier, vol. 31(11), pages 3377-3397, November.
    7. Stein, Elias M & Stein, Jeremy C, 1991. "Stock Price Distributions with Stochastic Volatility: An Analytic Approach," Review of Financial Studies, Society for Financial Studies, vol. 4(4), pages 727-52.
    8. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
    9. S. Benaim & P. Friz, 2009. "Regular Variation And Smile Asymptotics," Mathematical Finance, Wiley Blackwell, vol. 19(1), pages 1-12.
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