A Minimal Financial Market Model

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.