A Minimal Financial Market Model

Eckhard Platen ()

No 48, Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney

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.

Keywords: stochastic volatility; financial market model; derivative pricing; square root process (search for similar items in EconPapers)
JEL-codes: G10 G13 (search for similar items in EconPapers)
Date: 2001-03-01
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Citations: View citations in EconPapers (64)

Published as: Platen, E., 2001, "A Minimal Financial Market Model", Trends in Mathematics, 293-301.

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Working Paper: A minimal financial market model (2000)
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