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Option Pricing with Normal Mixture Returns: Modelling Excess Kurtosis and Uncertanity in Volatility

  • Carol Alexander


    (ICMA Centre, University of Reading)

  • Sujit Narayanan


    (ICMA Centre, University of Reading)

his paper addresses the problem of uncertainty in volatility, and how this affects option prices. The volatility uncertainty adjustment to Black-Scholes option prices is quantified in this paper using a normal mixture model for the distribution of underlying returns, or equivalently, assuming a mixture of lognormal densities for the density of the asset price. The use of a lognormal mixture price process for pricing options is not new (Ritchey, 1990) but the local volatility that should be used in the lognormal mixture price process has only recently been established (Brigo and Mercurio, 2000a, 2001).

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Paper provided by Henley Business School, Reading University in its series ICMA Centre Discussion Papers in Finance with number icma-dp2001-10.

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Length: 34 pages
Date of creation: Nov 2001
Date of revision: Dec 2001
Handle: RePEc:rdg:icmadp:icma-dp2001-10
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  1. Ritchey, Robert J, 1990. "Call Option Valuation for Discrete Normal Mixtures," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 13(4), pages 285-96, Winter.
  2. Kien Tran, 1998. "Estimating mixtures of normal distributions via empirical characteristic function," Econometric Reviews, Taylor & Francis Journals, vol. 17(2), pages 167-183.
  3. Goodhart, Charles A. E. & O'Hara, Maureen, 1997. "High frequency data in financial markets: Issues and applications," Journal of Empirical Finance, Elsevier, vol. 4(2-3), pages 73-114, June.
  4. Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394.
  5. Hsieh, David A., 1988. "The statistical properties of daily foreign exchange rates: 1974-1983," Journal of International Economics, Elsevier, vol. 24(1-2), pages 129-145, February.
  6. Baillie, Richard T & Bollerslev, Tim, 2002. "The Message in Daily Exchange Rates: A Conditional-Variance Tale," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 60-68, January.
  7. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  8. Muller, Ulrich A. & Dacorogna, Michel M. & Olsen, Richard B. & Pictet, Olivier V. & Schwarz, Matthias & Morgenegg, Claude, 1990. "Statistical study of foreign exchange rates, empirical evidence of a price change scaling law, and intraday analysis," Journal of Banking & Finance, Elsevier, vol. 14(6), pages 1189-1208, December.
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