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A Data-Reconstructed Fractional Volatility Model

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Author Info
Mendes, Rui Vilela
Oliveira, Maria J.

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Abstract

Based on criteria of mathematical simplicity and consistency with empirical market data, a stochastic volatility model is constructed, the volatility process being driven by fractional noise. Price return statistics and asymptotic behavior are derived from the model and compared with data. Deviations from Black-Scholes and a new option pricing formula are also obtained.

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Publisher Info
Paper provided by Kiel Institute for the World Economy in its series Economics Discussion Papers with number 2008-22.

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Date of creation: 2008
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Handle: RePEc:zbw:ifwedp:7284

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Related research
Keywords: Fractional noise; induced volatility; statistics of returns; option pricing;

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Find related papers by JEL classification:
C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies
G12 - Financial Economics - - General Financial Markets - - - Asset Pricing

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  1. 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. [Downloadable!] (restricted)
  2. Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring. [Downloadable!] (restricted)
  3. Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 145-166. [Downloadable!] (restricted)
  4. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June. [Downloadable!] (restricted)
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  5. 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. [Downloadable!] (restricted)
  6. Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.
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  7. A. Christian Silva & Richard E. Prange & Victor M. Yakovenko, 2004. "Exponential distribution of financial returns at mesoscopic time lags: a new stylized fact," Quantitative Finance Papers cond-mat/0401225, arXiv.org, revised Jul 2004. [Downloadable!]
  8. Breidt, F. Jay & Crato, Nuno & de Lima, Pedro, 1998. "The detection and estimation of long memory in stochastic volatility," Journal of Econometrics, Elsevier, vol. 83(1-2), pages 325-348. [Downloadable!] (restricted)
  9. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 6(2), pages 327-43. [Downloadable!] (restricted)
  10. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July. [Downloadable!] (restricted)
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