A minimal financial market model
The paper proposes a financial market model that generates stochastic volatility and stochastic interest rate using a minimal number of factors that characterise the dynamics of the different denominations of the deflator. It models asset prices essentially as functionals of square root and Ornstein-Uhlenbeek processes. The resulting price processes exhibit stochastic volatility with leptokurtic log-return distributions that c1osely match those observed in reality. The resulting index of the market is negatively correlated with its volatility which models the well-known leverage effect. The average growth rates of the different denominations of the deflator are Ornstein-Uhlenbeek processes which generates the typically observed long term Gaussianity of logreturns of asset prices.
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