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A Minimal Financial Market Model

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Author Info
Eckhard Platen () (School of Finance and Economics, University of Technology, Sydney)

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Abstract

The paper proposes a financial market model that generates stochastic volatilities and stochastic interest rates using a minimal number of factors that characterise the dynamics of different denominations of a benchmark portfolio. It models asset prices essentially as functionals of square root and Ornstein-Uhlenbeck processes. The resulting price processes exhibit stochastic volatility with leptokurtic log-return distributions that closely match those observed in reality. The benchmark portfolio is negatively correlated with its volatility which models the well-known leverage effect. The average growth rates of the different denominations of the benchmark portfolio are Ornstein-Uhlenbeck processes which generates the typically observed long term Gaussianity of log-returns of asset prices.

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Publisher Info
Paper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 48.

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Date of creation: 01 Mar 2001
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Handle: RePEc:uts:rpaper:48

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Related research
Keywords: stochastic volatility; financial market model; derivative pricing; square root process;

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Find related papers by JEL classification:
G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

  1. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-55, January. [Downloadable!] (restricted)
  2. Chan, K C, et al, 1992. " An Empirical Comparison of Alternative Models of the Short-Term Interest Rate," Journal of Finance, American Finance Association, vol. 47(3), pages 1209-27, July. [Downloadable!] (restricted)
  3. Frey, Rüdiger, 1997. "Derivative Asset Analysis in Models with Level-Dependent and Stochastic Volatility," Discussion Paper Serie B 401, University of Bonn, Germany. [Downloadable!]
  4. Eckhard Platen, 2000. "Risk Premia and Financial Modelling Without Measure Transformation," Research Paper Series 45, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
    Other versions:
  5. Simon Hurst & Eckhard Platen & Svetlozar Rachev, 1997. "Subordinated Market Index Models: A Comparison," Asia-Pacific Financial Markets, Springer, vol. 4(2), pages 97-124, May. [Downloadable!] (restricted)
  6. Eckhard Platen, 1999. "A short term interest rate model," Finance and Stochastics, Springer, vol. 3(2), pages 215-225. [Downloadable!] (restricted)
  7. 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)
  8. Ghysels, E. & Harvey, A. & Renault, E., 1996. "Stochastic Volatility," Cahiers de recherche 9613, Universite de Montreal, Departement de sciences economiques. [Downloadable!]
    Other versions:
  9. Eckhard Platen, 1999. "On the Log-Return Distribution of Index Benchmarked Share Prices," Research Paper Series 22, Quantitative Finance Research Centre, University of Technology, Sydney.
  10. Barndorf-Nielsen, O.E. & Shephard, N., 1998. "Aggregation and Model Construction for Volatility Models," Economics Papers 141, Economics Group, Nuffield College, University of Oxford.
  11. 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)
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