Asymptotic Formulas with Error Estimates for Call Pricing Functions and the Implied Volatility at Extreme Strikes
AbstractIn 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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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 0906.0394.
Date of creation: Jun 2009
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Web page: http://arxiv.org/
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- Archil Gulisashvili & Elias M. Stein, 2009. "Implied Volatility In The Hull-White Model," Mathematical Finance, Wiley Blackwell, vol. 19(2), pages 303-327.
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- S. Benaim & P. Friz, 2009. "Regular Variation And Smile Asymptotics," Mathematical Finance, Wiley Blackwell, vol. 19(1), pages 1-12.
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- 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.
- 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.
- Hans Buehler, 2006. "Expensive martingales," Quantitative Finance, Taylor & Francis Journals, vol. 6(3), pages 207-218.
- 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.
- Archil Gulisashvili & Josep Vives, 2010. "Two-sided estimates for stock price distribution densities in jump-diffusion models," Papers 1005.1917, arXiv.org.
- P. Friz & S. Gerhold & A. Gulisashvili & S. Sturm, 2010. "On refined volatility smile expansion in the Heston model," Papers 1001.3003, arXiv.org, revised Nov 2010.
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