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Higher-order volatility

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  • Carey, Alexander

Abstract

An important purpose of derivatives modelling is to provide practitioners with actionable measures of risk. The Black and Scholes volatility remains a favourite on trading floors in spite of well-known biases. One popular extension is to make volatility a function of time and the underlying asset price, as in local volatility models. This paper presents an alternative extension, which produces volatility-like quantities to address the skews and smiles found in most derivatives markets.

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File URL: http://mpra.ub.uni-muenchen.de/4993/
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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 4993.

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Date of creation: 01 Dec 2005
Date of revision:
Handle: RePEc:pra:mprapa:4993

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Related research

Keywords: higher-order volatility; higher-order moments; volatility smile; S&P 500;

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References

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  1. 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 637-54, May-June.
  2. Merton, Robert C., 1975. "Option pricing when underlying stock returns are discontinuous," Working papers 787-75., Massachusetts Institute of Technology (MIT), Sloan School of Management.
  3. Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring.
  4. Jarrow, Robert & Rudd, Andrew, 1982. "Approximate option valuation for arbitrary stochastic processes," Journal of Financial Economics, Elsevier, vol. 10(3), pages 347-369, November.
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Citations

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Cited by:
  1. Carey, Alexander, 2006. "Path-conditional forward volatility," MPRA Paper 4964, University Library of Munich, Germany.
  2. Carey, Alexander, 2006. "Higher-order volatility: dynamics and sensitivities," MPRA Paper 5009, University Library of Munich, Germany.
  3. Carey, Alexander, 2010. "Higher-order volatility: time series," MPRA Paper 21087, University Library of Munich, Germany.

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